diff --git a/coefs.h b/coefs.h index 338074d84a4d2486035b9dd198af3eb60c4bc3ac..8039197f92fb8647a0be806472e5b278f36116b4 100644 --- a/coefs.h +++ b/coefs.h @@ -25,6 +25,8 @@ struct COEFS std::vector<SC> v; std::vector<ex> basis; std::vector<ex> basis_tex; + std::vector<int> pow_dl; + std::vector<int> pow_dt; int order=6; // default void fill(ex &e); bool fill_recursive(ex &e, SC &sc, int level); diff --git a/core.cpp b/core.cpp index a980dac24521c58683a5a0d1dea12a633b7f63f2..d32fa87b8f49a9083bbd4f5e44b7d3d6aebf777d 100644 --- a/core.cpp +++ b/core.cpp @@ -153,6 +153,8 @@ void CORE::fill_sym_vels_to_basis(COEFS &CF) { CF.basis.push_back(sym_vel[d]); CF.basis_tex.push_back(sym_vel[d]); + CF.pow_dl.push_back(0); + CF.pow_dt.push_back(0); } if (use_tay_vels) @@ -165,6 +167,9 @@ void CORE::fill_sym_vels_to_basis(COEFS &CF) { for (int d=0;d<DIM;d++) { + CF.pow_dl.push_back(tay_vels[d]->get_pow_dl(k-j,j1,j2,j3)); + CF.pow_dt.push_back(tay_vels[d]->get_pow_dt(k-j,j1,j2,j3)); + CF.basis.push_back(tay_vels[d]->get_tay(k-j,j1,j2,j3)); CF.basis_tex.push_back(tay_vels[d]->get_tay_tex(k-j,j1,j2,j3)); } @@ -251,7 +256,7 @@ void CORE::allocate() { tay_vels = new TAYLOR*[DIM]; if (verbosity==1) printf("allocate tay_vels\n"); - for (int d=0;d<DIM;d++) tay_vels[d] = new TAYLOR(DIM,Q,ORDER,_index,Nindex); + for (int d=0;d<DIM;d++) tay_vels[d] = new TAYLOR(DIM,Q,ORDER,_index,Nindex,sym_dl,sym_dt); if (DIM>=1) tay_vels[0]->allocate("u", sym_vel[0]); if (DIM>=2) tay_vels[1]->allocate("v", sym_vel[1]); if (DIM>=3) tay_vels[2]->allocate("w", sym_vel[2]); @@ -350,7 +355,7 @@ void CORE::allocate() { if (use_tay_ms) { - tay_ms[q] = new TAYLOR(DIM,Q,ORDER,_index,Nindex); + tay_ms[q] = new TAYLOR(DIM,Q,ORDER,_index,Nindex,sym_dl,sym_dt); lbm.moment_symbol(desc2,q,Q); lbm.moment_symbol_number(desc3,q,Q); if (strlen(desc3)>0) @@ -361,7 +366,7 @@ void CORE::allocate() } if (use_tay_meqs) { - tay_meqs[q] = new TAYLOR(DIM,Q,ORDER,_index,Nindex); + tay_meqs[q] = new TAYLOR(DIM,Q,ORDER,_index,Nindex,sym_dl,sym_dt); sprintf(comp,"{{\\tilde m}^{eq}_{%d}}",q); tay_meqs[q]->allocate(comp,0); } @@ -1079,8 +1084,25 @@ void CORE::export_EPDE_coefs_bigprint(ex &expr, ofstream &fout, char* str) } if (none) fout << "1"; fout << "\\right]} }"; + + // put dl^pow dt^pow ... count all powers + int pow_dl=0; + int pow_dt=0; + if (order>0) { + for (int b=0;b<CF.basis.size();b++) + if (CF.v[i].exp[b] > 0) + { + pow_dl+=CF.pow_dl[b]*CF.v[i].exp[b]; + pow_dt+=CF.pow_dt[b]*CF.v[i].exp[b]; + } + // put dl^pow dt^pow + if (pow_dt==1) fout << "\\dt "; + if (pow_dt>1) fout << "\\dt^{"<< pow_dt <<"} "; + if (pow_dl==1) fout << "\\dl "; + if (pow_dl>1) fout << "\\dl^{"<< pow_dl <<"} "; + for (int b=0;b<CF.basis.size();b++) { if (CF.v[i].exp[b] != 0) @@ -1134,6 +1156,12 @@ void CORE::export_EPDE_coefs_bigprint(ex &expr, ofstream &fout, char* str) if (CF2.v[i2].order()==or2) outex += CF2.v[i2].coef * CF2.v[i2].base; + outex = expand(outex); + + // eliminate \dl and \dt from the coefficient + outex = subs(outex, sym_dl==1); + outex = subs(outex, sym_dt==1); + ostringstream s1; s1 << latex; if (factor_coefs) @@ -1196,6 +1224,14 @@ void CORE::export_EPDE_coefs(int pde) if (k-j>0) { if (k-j==1) sprintf(str_dt,"\\dt"); else sprintf(str_dt,"\\dt^{%d}",k-j); } else sprintf(str_dt,""); if (j>0) { if (j==1) sprintf(str_dl,"\\dl"); else sprintf(str_dl,"\\dl^{%d}",j); } else sprintf(str_dl,""); + // put dl^pow dt^pow + int pow_dl=tay_ms[q]->get_pow_dl(k-j,j1,j2,j3); + int pow_dt=tay_ms[q]->get_pow_dt(k-j,j1,j2,j3); + if (pow_dt==1) gout << "\\dt "; + if (pow_dt>1) gout << "\\dt^{"<< pow_dt <<"} "; + if (pow_dl==1) gout << "\\dl "; + if (pow_dl>1) gout << "\\dl^{"<< pow_dl <<"} "; + gout << tay_ms[q]->get_tay(k-j,j1,j2,j3) << endl; last_c_nonzero=count; count++; @@ -1216,7 +1252,7 @@ void CORE::export_EPDE_coefs(int pde) for (int j1=0;j1<=k;j1++) for (int q=0;q<Q;q++) if (j1+j2+j3==j) - if (coefs_epde[pde][k-j][indO(j1,j2,j3)]!=0) + if (coefs_epde[pde][q][k-j][indO(j1,j2,j3)]!=0) max++; count=0; diff --git a/core.h b/core.h index d520cf6e6c4a7ac6dbb4d362cf1e0df4025a4e6a..bce6b73b5156e92725aa0763b6e52a0ae8d8dc62 100644 --- a/core.h +++ b/core.h @@ -66,6 +66,9 @@ struct CORE : DEF // central values: ex *sym_m, *sym_meq, *sym_f, *sym_feq; + ex sym_dl=symbol("\\dl"); + ex sym_dt=symbol("\\dt"); + TAYLOR **tay_vels, **tay_ms, **tay_meqs; matrix const_feq, const_sub_feq, const_meq; diff --git a/lbm.cpp b/lbm.cpp index ef5c1e61662c8d96af0e84c3f628bdbdedef7c17..bb2dee1b704581cfa0ea9c29dfad0bc40ff1f4d4 100644 --- a/lbm.cpp +++ b/lbm.cpp @@ -76,13 +76,13 @@ void LBM::setA_MRT1(matrix &A, int Q, ex u, ex v, ex w) A(4,4) = n1o2*sym_os[4]+n1o2*sym_os[2]; break; case 7: - A(0,0) = 0; - A(0,1) = -sym_os[4]; - A(0,2) = -sym_os[5]; - A(0,3) = -sym_os[6]; - A(0,4) = -sym_os[4]; - A(0,5) = -sym_os[5]; - A(0,6) = -sym_os[6]; + A(0,0) = sym_os[0]; + A(0,0) = sym_os[0]-sym_os[4]; + A(0,0) = sym_os[0]-sym_os[5]; + A(0,0) = sym_os[0]-sym_os[6]; + A(0,0) = sym_os[0]-sym_os[4]; + A(0,0) = sym_os[0]-sym_os[5]; + A(0,0) = sym_os[0]-sym_os[6]; A(1,0) = 0; A(1,1) = n1o2*sym_os[4]+n1o2*sym_os[1]; A(1,2) = 0; @@ -127,15 +127,15 @@ void LBM::setA_MRT1(matrix &A, int Q, ex u, ex v, ex w) A(6,6) = n1o2*sym_os[6]+n1o2*sym_os[3]; break; case 9: - A(0,0)=0; - A(0,1)=-sym_os[4]; - A(0,2)=-sym_os[5]; - A(0,3)=-sym_os[4]; - A(0,4)=-sym_os[5]; - A(0,5)=sym_os[8]-sym_os[5]-sym_os[4]; - A(0,6)=sym_os[8]-sym_os[5]-sym_os[4]; - A(0,7)=sym_os[8]-sym_os[5]-sym_os[4]; - A(0,8)=sym_os[8]-sym_os[5]-sym_os[4]; + A(0,0)=sym_os[0]; + A(0,1)=sym_os[0]-sym_os[4]; + A(0,2)=sym_os[0]-sym_os[5]; + A(0,3)=sym_os[0]-sym_os[4]; + A(0,4)=sym_os[0]-sym_os[5]; + A(0,5)=sym_os[8]-sym_os[5]-sym_os[4]+sym_os[0]; + A(0,6)=sym_os[8]-sym_os[5]-sym_os[4]+sym_os[0]; + A(0,7)=sym_os[8]-sym_os[5]-sym_os[4]+sym_os[0]; + A(0,8)=sym_os[8]-sym_os[5]-sym_os[4]+sym_os[0]; A(1,0)=0; A(1,1)=sym_os[4]/2+sym_os[1]/2; A(1,2)=0; @@ -250,55 +250,61 @@ void LBM::setA_MRT2(matrix &A, int Q, ex u, ex v, ex w) A(4,4) = n1o4*sym_os[4]+n1o4*sym_os[3]+n1o2*sym_os[2]; break; case 7: - A(0,0) = 0; - A(0,1) = -sym_os[4]; - A(0,2) = -sym_os[4]; - A(0,3) = -sym_os[4]; - A(0,4) = -sym_os[4]; - A(0,5) = -sym_os[4]; - A(0,6) = -sym_os[4]; + A(0,0) = sym_os[0]; + A(0,1) = sym_os[0]-sym_os[4]; + A(0,2) = sym_os[0]-sym_os[4]; + A(0,3) = sym_os[0]-sym_os[4]; + A(0,4) = sym_os[0]-sym_os[4]; + A(0,5) = sym_os[0]-sym_os[4]; + A(0,6) = sym_os[0]-sym_os[4]; + A(1,0) = 0; - A(1,1) = n1o6*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]+n1o2*sym_os[1]; - A(1,2) = n1o6*sym_os[4]-n1o6*sym_os[5]; - A(1,3) = n1o6*sym_os[4]-n1o6*sym_os[6]; - A(1,4) = n1o6*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]-n1o2*sym_os[1]; - A(1,5) = n1o6*sym_os[4]-n1o6*sym_os[5]; - A(1,6) = n1o6*sym_os[4]-n1o6*sym_os[6]; + A(1,1) = sym_os[6]/6+sym_os[5]/6+sym_os[4]/6+sym_os[1]/2; + A(1,2) = sym_os[4]/6-sym_os[5]/6; + A(1,3) = sym_os[4]/6-sym_os[6]/6; + A(1,4) = sym_os[6]/6+sym_os[5]/6+sym_os[4]/6-sym_os[1]/2; + A(1,5) = sym_os[4]/6-sym_os[5]/6; + A(1,6) = sym_os[4]/6-sym_os[6]/6; + A(2,0) = 0; - A(2,1) = n1o6*sym_os[6]-n1o3*sym_os[5]+n1o6*sym_os[4]; - A(2,2) = n1o3*sym_os[5]+n1o6*sym_os[4]+n1o2*sym_os[2]; - A(2,3) = n1o6*sym_os[4]-n1o6*sym_os[6]; - A(2,4) = n1o6*sym_os[6]-n1o3*sym_os[5]+n1o6*sym_os[4]; - A(2,5) = n1o3*sym_os[5]+n1o6*sym_os[4]-n1o2*sym_os[2]; - A(2,6) = n1o6*sym_os[4]-n1o6*sym_os[6]; + A(2,1) = sym_os[6]/6-sym_os[5]/3+sym_os[4]/6; + A(2,2) = sym_os[5]/3+sym_os[4]/6+sym_os[2]/2; + A(2,3) = sym_os[4]/6-sym_os[6]/6; + A(2,4) = sym_os[6]/6-sym_os[5]/3+sym_os[4]/6; + A(2,5) = sym_os[5]/3+sym_os[4]/6-sym_os[2]/2; + A(2,6) = sym_os[4]/6-sym_os[6]/6; + A(3,0) = 0; - A(3,1) = -n1o3*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]; - A(3,2) = n1o6*sym_os[4]-n1o6*sym_os[5]; - A(3,3) = n1o3*sym_os[6]+n1o6*sym_os[4]+n1o2*sym_os[3]; - A(3,4) = -n1o3*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]; - A(3,5) = n1o6*sym_os[4]-n1o6*sym_os[5]; - A(3,6) = n1o3*sym_os[6]+n1o6*sym_os[4]-n1o2*sym_os[3]; + A(3,1) = -sym_os[6]/3+sym_os[5]/6+sym_os[4]/6; + A(3,2) = sym_os[4]/6-sym_os[5]/6; + A(3,3) = sym_os[6]/3+sym_os[4]/6+sym_os[3]/2; + A(3,4) = -sym_os[6]/3+sym_os[5]/6+sym_os[4]/6; + A(3,5) = sym_os[4]/6-sym_os[5]/6; + A(3,6) = sym_os[6]/3+sym_os[4]/6-sym_os[3]/2; + A(4,0) = 0; - A(4,1) = n1o6*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]-n1o2*sym_os[1]; - A(4,2) = n1o6*sym_os[4]-n1o6*sym_os[5]; - A(4,3) = n1o6*sym_os[4]-n1o6*sym_os[6]; - A(4,4) = n1o6*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]+n1o2*sym_os[1]; - A(4,5) = n1o6*sym_os[4]-n1o6*sym_os[5]; - A(4,6) = n1o6*sym_os[4]-n1o6*sym_os[6]; + A(4,1) = sym_os[6]/6+sym_os[5]/6+sym_os[4]/6-sym_os[1]/2; + A(4,2) = sym_os[4]/6-sym_os[5]/6; + A(4,3) = sym_os[4]/6-sym_os[6]/6; + A(4,4) = sym_os[6]/6+sym_os[5]/6+sym_os[4]/6+sym_os[1]/2; + A(4,5) = sym_os[4]/6-sym_os[5]/6; + A(4,6) = sym_os[4]/6-sym_os[6]/6; + A(5,0) = 0; - A(5,1) = n1o6*sym_os[6]-n1o3*sym_os[5]+n1o6*sym_os[4]; - A(5,2) = n1o3*sym_os[5]+n1o6*sym_os[4]-n1o2*sym_os[2]; - A(5,3) = n1o6*sym_os[4]-n1o6*sym_os[6]; - A(5,4) = n1o6*sym_os[6]-n1o3*sym_os[5]+n1o6*sym_os[4]; - A(5,5) = n1o3*sym_os[5]+n1o6*sym_os[4]+n1o2*sym_os[2]; - A(5,6) = n1o6*sym_os[4]-n1o6*sym_os[6]; + A(5,1) = sym_os[6]/6-sym_os[5]/3+sym_os[4]/6; + A(5,2) = sym_os[5]/3+sym_os[4]/6-sym_os[2]/2; + A(5,3) = sym_os[4]/6-sym_os[6]/6; + A(5,4) = sym_os[6]/6-sym_os[5]/3+sym_os[4]/6; + A(5,5) = sym_os[5]/3+sym_os[4]/6+sym_os[2]/2; + A(5,6) = sym_os[4]/6-sym_os[6]/6; + A(6,0) = 0; - A(6,1) = -n1o3*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]; - A(6,2) = n1o6*sym_os[4]-n1o6*sym_os[5]; - A(6,3) = n1o3*sym_os[6]+n1o6*sym_os[4]-n1o2*sym_os[3]; - A(6,4) = -n1o3*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]; - A(6,5) = n1o6*sym_os[4]-n1o6*sym_os[5]; - A(6,6) = n1o3*sym_os[6]+n1o6*sym_os[4]+n1o2*sym_os[3]; + A(6,1) = -sym_os[6]/3+sym_os[5]/6+sym_os[4]/6; + A(6,2) = sym_os[4]/6-sym_os[5]/6; + A(6,3) = sym_os[6]/3+sym_os[4]/6-sym_os[3]/2; + A(6,4) = -sym_os[6]/3+sym_os[5]/6+sym_os[4]/6; + A(6,5) = sym_os[4]/6-sym_os[5]/6; + A(6,6) = sym_os[6]/3+sym_os[4]/6+sym_os[3]/2; break; default: printf("Error: matrix A not implemented for Q%d and MRT2\n",Q); @@ -349,143 +355,148 @@ void LBM::setA_CLBM1(matrix &A, int Q, ex u, ex v, ex w) A(4,4) = n1o2*(sym_os[4]-2*sym_os[2]+sym_os[0])*v*v+n1o2*(2*sym_os[4]-sym_os[2]-sym_os[0])*v+n1o2*sym_os[4]+n1o2*sym_os[2]; break; case 7: - A(0,0) = (2*sym_os[3]-sym_os[6])*w*w+(2*sym_os[2]-sym_os[5])*v*v+(2*sym_os[1]-sym_os[4])*u*u; - A(0,1) = (2*sym_os[3]-sym_os[6])*w*w+(2*sym_os[2]-sym_os[5])*v*v+(2*sym_os[1]-sym_os[4])*u*u+(2*sym_os[4]-2*sym_os[1])*u-sym_os[4]; - A(0,2) = (2*sym_os[3]-sym_os[6])*w*w+(2*sym_os[2]-sym_os[5])*v*v+(2*sym_os[5]-2*sym_os[2])*v+(2*sym_os[1]-sym_os[4])*u*u-sym_os[5]; - A(0,3) = (2*sym_os[3]-sym_os[6])*w*w+(2*sym_os[6]-2*sym_os[3])*w+(2*sym_os[2]-sym_os[5])*v*v+(2*sym_os[1]-sym_os[4])*u*u-sym_os[6]; - A(0,4) = (2*sym_os[3]-sym_os[6])*w*w+(2*sym_os[2]-sym_os[5])*v*v+(2*sym_os[1]-sym_os[4])*u*u+(2*sym_os[1]-2*sym_os[4])*u-sym_os[4]; - A(0,5) = (2*sym_os[3]-sym_os[6])*w*w+(2*sym_os[2]-sym_os[5])*v*v+(2*sym_os[2]-2*sym_os[5])*v+(2*sym_os[1]-sym_os[4])*u*u-sym_os[5]; - A(0,6) = (2*sym_os[3]-sym_os[6])*w*w+(2*sym_os[3]-2*sym_os[6])*w+(2*sym_os[2]-sym_os[5])*v*v+(2*sym_os[1]-sym_os[4])*u*u-sym_os[6]; - A(1,0) = n1o2*(sym_os[4]-2*sym_os[1])*u*u-n1o2*sym_os[1]*u; - A(1,1) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*(sym_os[1]-2*sym_os[4])*u+n1o2*sym_os[4]+n1o2*sym_os[1]; - A(1,2) = n1o2*(sym_os[4]-2*sym_os[1])*u*u-n1o2*sym_os[1]*u; - A(1,3) = n1o2*(sym_os[4]-2*sym_os[1])*u*u-n1o2*sym_os[1]*u; - A(1,4) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*(2*sym_os[4]-3*sym_os[1])*u+n1o2*sym_os[4]-n1o2*sym_os[1]; - A(1,5) = n1o2*(sym_os[4]-2*sym_os[1])*u*u-n1o2*sym_os[1]*u; - A(1,6) = n1o2*(sym_os[4]-2*sym_os[1])*u*u-n1o2*sym_os[1]*u; - A(2,0) = n1o2*(sym_os[5]-2*sym_os[2])*v*v-n1o2*sym_os[2]*v; - A(2,1) = n1o2*(sym_os[5]-2*sym_os[2])*v*v-n1o2*sym_os[2]*v; - A(2,2) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*(sym_os[2]-2*sym_os[5])*v+n1o2*sym_os[5]+n1o2*sym_os[2]; - A(2,3) = n1o2*(sym_os[5]-2*sym_os[2])*v*v-n1o2*sym_os[2]*v; - A(2,4) = n1o2*(sym_os[5]-2*sym_os[2])*v*v-n1o2*sym_os[2]*v; - A(2,5) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*(2*sym_os[5]-3*sym_os[2])*v+n1o2*sym_os[5]-n1o2*sym_os[2]; - A(2,6) = n1o2*(sym_os[5]-2*sym_os[2])*v*v-n1o2*sym_os[2]*v; - A(3,0) = n1o2*(sym_os[6]-2*sym_os[3])*w*w-n1o2*sym_os[3]*w; - A(3,1) = n1o2*(sym_os[6]-2*sym_os[3])*w*w-n1o2*sym_os[3]*w; - A(3,2) = n1o2*(sym_os[6]-2*sym_os[3])*w*w-n1o2*sym_os[3]*w; - A(3,3) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*(sym_os[3]-2*sym_os[6])*w+n1o2*sym_os[6]+n1o2*sym_os[3]; - A(3,4) = n1o2*(sym_os[6]-2*sym_os[3])*w*w-n1o2*sym_os[3]*w; - A(3,5) = n1o2*(sym_os[6]-2*sym_os[3])*w*w-n1o2*sym_os[3]*w; - A(3,6) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*(2*sym_os[6]-3*sym_os[3])*w+n1o2*sym_os[6]-n1o2*sym_os[3]; - A(4,0) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*sym_os[1]*u; - A(4,1) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*(3*sym_os[1]-2*sym_os[4])*u+n1o2*sym_os[4]-n1o2*sym_os[1]; - A(4,2) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*sym_os[1]*u; - A(4,3) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*sym_os[1]*u; - A(4,4) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*(2*sym_os[4]-sym_os[1])*u+n1o2*sym_os[4]+n1o2*sym_os[1]; - A(4,5) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*sym_os[1]*u; - A(4,6) = n1o2*(sym_os[4]-2*sym_os[1])*u*u+n1o2*sym_os[1]*u; - A(5,0) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*sym_os[2]*v; - A(5,1) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*sym_os[2]*v; - A(5,2) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*(3*sym_os[2]-2*sym_os[5])*v+n1o2*sym_os[5]-n1o2*sym_os[2]; - A(5,3) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*sym_os[2]*v; - A(5,4) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*sym_os[2]*v; - A(5,5) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*(2*sym_os[5]-sym_os[2])*v+n1o2*sym_os[5]+n1o2*sym_os[2]; - A(5,6) = n1o2*(sym_os[5]-2*sym_os[2])*v*v+n1o2*sym_os[2]*v; - A(6,0) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*sym_os[3]*w; - A(6,1) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*sym_os[3]*w; - A(6,2) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*sym_os[3]*w; - A(6,3) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*(3*sym_os[3]-2*sym_os[6])*w+n1o2*sym_os[6]-n1o2*sym_os[3]; - A(6,4) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*sym_os[3]*w; - A(6,5) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*sym_os[3]*w; - A(6,6) = n1o2*(sym_os[6]-2*sym_os[3])*w*w+n1o2*(2*sym_os[6]-sym_os[3])*w+n1o2*sym_os[6]+n1o2*sym_os[3]; + A(0,0) = (-sym_os[6]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[5]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u+sym_os[0]; + A(0,1) = (-sym_os[6]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[5]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u+(2*sym_os[4]-2*sym_os[1])*u-sym_os[4]+sym_os[0]; + A(0,2) = (-sym_os[6]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[5]+2*sym_os[2]-sym_os[0])*v*v+(2*sym_os[5]-2*sym_os[2])*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u-sym_os[5]+sym_os[0]; + A(0,3) = (-sym_os[6]+2*sym_os[3]-sym_os[0])*w*w+(2*sym_os[6]-2*sym_os[3])*w+(-sym_os[5]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u-sym_os[6]+sym_os[0]; + A(0,4) = (-sym_os[6]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[5]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u+(2*sym_os[1]-2*sym_os[4])*u-sym_os[4]+sym_os[0]; + A(0,5) = (-sym_os[6]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[5]+2*sym_os[2]-sym_os[0])*v*v+(2*sym_os[2]-2*sym_os[5])*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u-sym_os[5]+sym_os[0]; + A(0,6) = (-sym_os[6]+2*sym_os[3]-sym_os[0])*w*w+(2*sym_os[3]-2*sym_os[6])*w+(-sym_os[5]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u-sym_os[6]+sym_os[0]; + + A(1,0) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[0]-sym_os[1])*u)*n1o2; + A(1,1) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(-2*sym_os[4]+sym_os[1]+sym_os[0])*u+sym_os[4]+sym_os[1])*n1o2; + A(1,2) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[0]-sym_os[1])*u)*n1o2; + A(1,3) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[0]-sym_os[1])*u)*n1o2; + A(1,4) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(2*sym_os[4]-3*sym_os[1]+sym_os[0])*u+sym_os[4]-sym_os[1])*n1o2; + A(1,5) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[0]-sym_os[1])*u)*n1o2; + A(1,6) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[0]-sym_os[1])*u)*n1o2; + + A(2,0) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[0]-sym_os[2])*v)*n1o2; + A(2,1) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[0]-sym_os[2])*v)*n1o2; + A(2,2) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(-2*sym_os[5]+sym_os[2]+sym_os[0])*v+sym_os[5]+sym_os[2])*n1o2; + A(2,3) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[0]-sym_os[2])*v)*n1o2; + A(2,4) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[0]-sym_os[2])*v)*n1o2; + A(2,5) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(2*sym_os[5]-3*sym_os[2]+sym_os[0])*v+sym_os[5]-sym_os[2])*n1o2; + A(2,6) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[0]-sym_os[2])*v)*n1o2; + + A(3,0) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[0]-sym_os[3])*w)*n1o2; + A(3,1) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[0]-sym_os[3])*w)*n1o2; + A(3,2) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[0]-sym_os[3])*w)*n1o2; + A(3,3) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(-2*sym_os[6]+sym_os[3]+sym_os[0])*w+sym_os[6]+sym_os[3])*n1o2; + A(3,4) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[0]-sym_os[3])*w)*n1o2; + A(3,5) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[0]-sym_os[3])*w)*n1o2; + A(3,6) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(2*sym_os[6]-3*sym_os[3]+sym_os[0])*w+sym_os[6]-sym_os[3])*n1o2; + + A(4,0) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[1]-sym_os[0])*u)*n1o2; + A(4,1) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(-2*sym_os[4]+3*sym_os[1]-sym_os[0])*u+sym_os[4]-sym_os[1])*n1o2; + A(4,2) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[1]-sym_os[0])*u)*n1o2; + A(4,3) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[1]-sym_os[0])*u)*n1o2; + A(4,4) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(2*sym_os[4]-sym_os[1]-sym_os[0])*u+sym_os[4]+sym_os[1])*n1o2; + A(4,5) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[1]-sym_os[0])*u)*n1o2; + A(4,6) = ((sym_os[4]-2*sym_os[1]+sym_os[0])*u*u+(sym_os[1]-sym_os[0])*u)*n1o2; + + A(5,0) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[2]-sym_os[0])*v)*n1o2; + A(5,1) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[2]-sym_os[0])*v)*n1o2; + A(5,2) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(-2*sym_os[5]+3*sym_os[2]-sym_os[0])*v+sym_os[5]-sym_os[2])*n1o2; + A(5,3) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[2]-sym_os[0])*v)*n1o2; + A(5,4) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[2]-sym_os[0])*v)*n1o2; + A(5,5) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(2*sym_os[5]-sym_os[2]-sym_os[0])*v+sym_os[5]+sym_os[2])*n1o2; + A(5,6) = ((sym_os[5]-2*sym_os[2]+sym_os[0])*v*v+(sym_os[2]-sym_os[0])*v)*n1o2; + + A(6,0) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[3]-sym_os[0])*w)*n1o2; + A(6,1) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[3]-sym_os[0])*w)*n1o2; + A(6,2) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[3]-sym_os[0])*w)*n1o2; + A(6,3) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(-2*sym_os[6]+3*sym_os[3]-sym_os[0])*w+sym_os[6]-sym_os[3])*n1o2; + A(6,4) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[3]-sym_os[0])*w)*n1o2; + A(6,5) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(sym_os[3]-sym_os[0])*w)*n1o2; + A(6,6) = ((sym_os[6]-2*sym_os[3]+sym_os[0])*w*w+(2*sym_os[6]-sym_os[3]-sym_os[0])*w+sym_os[6]+sym_os[3])*n1o2; break; case 9: - A(0,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+2*sym_os[4]-4*sym_os[2])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-4*sym_os[1])*u*u)/2; - A(0,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+(sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+(4*sym_os[1]-4*sym_os[4])*u+2*sym_os[4])/2; - A(0,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u-4*sym_os[4]+4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+2*sym_os[4])/2; - A(0,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+(sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+(4*sym_os[4]-4*sym_os[1])*u+2*sym_os[4])/2; - A(0,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+4*sym_os[4]-4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+2*sym_os[4])/2; - A(0,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+8*sym_os[7]+8*sym_os[6]-8*sym_os[3])*u+4*sym_os[8]-4*sym_os[6]-4*sym_os[4]+4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[4]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[4])/2; - A(0,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-8*sym_os[7]-8*sym_os[6]+8*sym_os[3])*u+4*sym_os[8]-4*sym_os[6]-4*sym_os[4]+4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[4]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[4])/2; - A(0,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+8*sym_os[7]+8*sym_os[6]-8*sym_os[3])*u-4*sym_os[8]+4*sym_os[6]+4*sym_os[4]-4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[4]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[4])/2; - A(0,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-8*sym_os[7]-8*sym_os[6]+8*sym_os[3])*u-4*sym_os[8]+4*sym_os[6]+4*sym_os[4]-4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[4]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[4])/2; - A(1,0)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u-sym_os[5]+sym_os[4])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+(sym_os[5]+sym_os[4]-4*sym_os[1])*u*u-2*sym_os[1]*u)/4; - A(1,1)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+(2*sym_os[4]-4*sym_os[1])*u*u+((-sym_os[5])-3*sym_os[4]+2*sym_os[1])*u+sym_os[5]+sym_os[4]+2*sym_os[1])/4; - A(1,2)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u)*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+4*sym_os[3]-4*sym_os[2])*u+2*sym_os[5]-2*sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])*u-sym_os[5]+sym_os[4])/4; - A(1,3)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+(4*sym_os[5]-2*sym_os[4]-4*sym_os[1])*u*u+(3*sym_os[5]+sym_os[4]-6*sym_os[1])*u+sym_os[5]+sym_os[4]-2*sym_os[1])/4; - A(1,4)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u)*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-4*sym_os[3]+4*sym_os[2])*u-2*sym_os[5]+2*sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])*u-sym_os[5]+sym_os[4])/4; - A(1,5)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+4*sym_os[7]+8*sym_os[6]+2*sym_os[5]+2*sym_os[4]-4*sym_os[3]-4*sym_os[2])*u+4*sym_os[8]+4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]-4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-2*sym_os[5]-4*sym_os[4]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[4]+2*sym_os[1])/4; - A(1,6)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-12*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2])*u+4*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+3*sym_os[5]-3*sym_os[4]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+2*sym_os[5]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[4]-2*sym_os[1])/4; - A(1,7)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+12*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2])*u-4*sym_os[8]+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+3*sym_os[5]-3*sym_os[4]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+2*sym_os[5]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[4]-2*sym_os[1])/4; - A(1,8)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-4*sym_os[7]-8*sym_os[6]-2*sym_os[5]-2*sym_os[4]+4*sym_os[3]+4*sym_os[2])*u-4*sym_os[8]-4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]+4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-2*sym_os[5]-4*sym_os[4]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[4]+2*sym_os[1])/4; - A(2,0)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u-2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u)/4; - A(2,1)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+4*sym_os[3]-4*sym_os[1])*u+2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+(2*sym_os[5]-2*sym_os[4])*u-sym_os[5]+sym_os[4])/4; - A(2,2)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+2*sym_os[4]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u-sym_os[5]-3*sym_os[4]+2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+sym_os[5]+sym_os[4]+2*sym_os[2])/4; - A(2,3)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-4*sym_os[3]+4*sym_os[1])*u+2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+(2*sym_os[4]-2*sym_os[5])*u-sym_os[5]+sym_os[4])/4; - A(2,4)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+4*sym_os[5]-2*sym_os[4]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+3*sym_os[5]+sym_os[4]-6*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+sym_os[5]+sym_os[4]-2*sym_os[2])/4; - A(2,5)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]+2*sym_os[4]-4*sym_os[3]-4*sym_os[1])*u+4*sym_os[8]-2*sym_os[6]-2*sym_os[5]-4*sym_os[4]+2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]+4*sym_os[6]+2*sym_os[5]-2*sym_os[4]-4*sym_os[3])*u-2*sym_os[8]-2*sym_os[6]+2*sym_os[4]+2*sym_os[2])/4; - A(2,6)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]-2*sym_os[4]+4*sym_os[3]+4*sym_os[1])*u+4*sym_os[8]-2*sym_os[6]-2*sym_os[5]-4*sym_os[4]+2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]-4*sym_os[6]-2*sym_os[5]+2*sym_os[4]+4*sym_os[3])*u-2*sym_os[8]-2*sym_os[6]+2*sym_os[4]+2*sym_os[2])/4; - A(2,7)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]+3*sym_os[5]-3*sym_os[4]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+8*sym_os[7]+12*sym_os[6]-2*sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[1])*u-4*sym_os[8]+6*sym_os[6]+2*sym_os[5]-6*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-4*sym_os[3])*u-2*sym_os[8]+2*sym_os[6]+2*sym_os[4]-2*sym_os[2])/4; - A(2,8)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]+3*sym_os[5]-3*sym_os[4]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-8*sym_os[7]-12*sym_os[6]+2*sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[1])*u-4*sym_os[8]+6*sym_os[6]+2*sym_os[5]-6*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+4*sym_os[3])*u-2*sym_os[8]+2*sym_os[6]+2*sym_os[4]-2*sym_os[2])/4; - A(3,0)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u-sym_os[5]+sym_os[4])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+(sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+2*sym_os[1]*u)/4; - A(3,1)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+(4*sym_os[5]-2*sym_os[4]-4*sym_os[1])*u*u+((-3*sym_os[5])-sym_os[4]+6*sym_os[1])*u+sym_os[5]+sym_os[4]-2*sym_os[1])/4; - A(3,2)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u)*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-4*sym_os[3]+4*sym_os[2])*u+2*sym_os[5]-2*sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+2*sym_os[1])*u-sym_os[5]+sym_os[4])/4; - A(3,3)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+(2*sym_os[4]-4*sym_os[1])*u*u+(sym_os[5]+3*sym_os[4]-2*sym_os[1])*u+sym_os[5]+sym_os[4]+2*sym_os[1])/4; - A(3,4)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u)*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+4*sym_os[3]-4*sym_os[2])*u-2*sym_os[5]+2*sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+2*sym_os[1])*u-sym_os[5]+sym_os[4])/4; - A(3,5)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+12*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2])*u+4*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+3*sym_os[5]-3*sym_os[4]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-2*sym_os[5]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[4]-2*sym_os[1])/4; - A(3,6)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-4*sym_os[7]-8*sym_os[6]-2*sym_os[5]-2*sym_os[4]+4*sym_os[3]+4*sym_os[2])*u+4*sym_os[8]+4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]-4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+2*sym_os[5]+4*sym_os[4]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[4]+2*sym_os[1])/4; - A(3,7)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+4*sym_os[7]+8*sym_os[6]+2*sym_os[5]+2*sym_os[4]-4*sym_os[3]-4*sym_os[2])*u-4*sym_os[8]-4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]+4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+2*sym_os[5]+4*sym_os[4]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[4]+2*sym_os[1])/4; - A(3,8)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-12*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2])*u-4*sym_os[8]+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+3*sym_os[5]-3*sym_os[4]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-2*sym_os[5]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[4]-2*sym_os[1])/4; - A(4,0)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u)/4; - A(4,1)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-4*sym_os[3]+4*sym_os[1])*u-2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+(2*sym_os[5]-2*sym_os[4])*u-sym_os[5]+sym_os[4])/4; - A(4,2)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+4*sym_os[5]-2*sym_os[4]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u-3*sym_os[5]-sym_os[4]+6*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+sym_os[5]+sym_os[4]-2*sym_os[2])/4; - A(4,3)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+4*sym_os[3]-4*sym_os[1])*u-2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+(2*sym_os[4]-2*sym_os[5])*u-sym_os[5]+sym_os[4])/4; - A(4,4)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+2*sym_os[4]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+sym_os[5]+3*sym_os[4]-2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+sym_os[5]+sym_os[4]+2*sym_os[2])/4; - A(4,5)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]+3*sym_os[5]-3*sym_os[4]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+8*sym_os[7]+12*sym_os[6]-2*sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[1])*u+4*sym_os[8]-6*sym_os[6]-2*sym_os[5]+6*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+4*sym_os[3])*u-2*sym_os[8]+2*sym_os[6]+2*sym_os[4]-2*sym_os[2])/4; - A(4,6)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]+3*sym_os[5]-3*sym_os[4]-4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-8*sym_os[7]-12*sym_os[6]+2*sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[1])*u+4*sym_os[8]-6*sym_os[6]-2*sym_os[5]+6*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-4*sym_os[3])*u-2*sym_os[8]+2*sym_os[6]+2*sym_os[4]-2*sym_os[2])/4; - A(4,7)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]+2*sym_os[4]-4*sym_os[3]-4*sym_os[1])*u-4*sym_os[8]+2*sym_os[6]+2*sym_os[5]+4*sym_os[4]-2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]-4*sym_os[6]-2*sym_os[5]+2*sym_os[4]+4*sym_os[3])*u-2*sym_os[8]-2*sym_os[6]+2*sym_os[4]+2*sym_os[2])/4; - A(4,8)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]-2*sym_os[4]+4*sym_os[3]+4*sym_os[1])*u-4*sym_os[8]+2*sym_os[6]+2*sym_os[5]+4*sym_os[4]-2*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]+4*sym_os[6]+2*sym_os[5]-2*sym_os[4]-4*sym_os[3])*u-2*sym_os[8]-2*sym_os[6]+2*sym_os[4]+2*sym_os[2])/4; - A(5,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u)*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[3])+2*sym_os[2]+2*sym_os[1])*u)*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u)/8; - A(5,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+2*sym_os[3]+2*sym_os[2]-2*sym_os[1])*u+2*sym_os[6]-sym_os[5]-sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+(sym_os[4]-sym_os[5])*u*u+(sym_os[5]-sym_os[4])*u)/8; - A(5,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u-sym_os[5]+sym_os[4])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+2*sym_os[3]-2*sym_os[2]+2*sym_os[1])*u+sym_os[5]-sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[3]-2*sym_os[2])*u)/8; - A(5,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2]+6*sym_os[1])*u+2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u+(sym_os[5]-sym_os[4])*u)/8; - A(5,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u+3*sym_os[5]-3*sym_os[4])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]+6*sym_os[2]+2*sym_os[1])*u+sym_os[5]-sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[3]+2*sym_os[2])*u)/8; - A(5,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+4*sym_os[7]+4*sym_os[6]+4*sym_os[5]+4*sym_os[4]-2*sym_os[3]-2*sym_os[2]-2*sym_os[1])*u+4*sym_os[8]+4*sym_os[7]-2*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; - A(5,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-12*sym_os[7]-4*sym_os[6]+6*sym_os[3]-2*sym_os[2]+6*sym_os[1])*u+4*sym_os[8]-4*sym_os[7]-2*sym_os[6]-2*sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]-4*sym_os[6]-2*sym_os[4]+6*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; - A(5,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+12*sym_os[7]+12*sym_os[6]-4*sym_os[5]-4*sym_os[4]-18*sym_os[3]+6*sym_os[2]+6*sym_os[1])*u-4*sym_os[8]+4*sym_os[7]+6*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]+4*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; - A(5,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-4*sym_os[7]-12*sym_os[6]+6*sym_os[3]+6*sym_os[2]-2*sym_os[1])*u-4*sym_os[8]-4*sym_os[7]+6*sym_os[6]-2*sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]-4*sym_os[6]-2*sym_os[4]+2*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; - A(6,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u)*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[3]-2*sym_os[2]-2*sym_os[1])*u)*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u)/8; - A(6,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]-2*sym_os[2]-6*sym_os[1])*u+2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u+(sym_os[4]-sym_os[5])*u)/8; - A(6,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u-sym_os[5]+sym_os[4])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-2*sym_os[3]+2*sym_os[2]-2*sym_os[1])*u+sym_os[5]-sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]-2*sym_os[3]+2*sym_os[2])*u)/8; - A(6,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2]+2*sym_os[1])*u+2*sym_os[6]-sym_os[5]-sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+(sym_os[4]-sym_os[5])*u*u+(sym_os[4]-sym_os[5])*u)/8; - A(6,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u+3*sym_os[5]-3*sym_os[4])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]-6*sym_os[2]-2*sym_os[1])*u+sym_os[5]-sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+2*sym_os[3]-2*sym_os[2])*u)/8; - A(6,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+12*sym_os[7]+4*sym_os[6]-6*sym_os[3]+2*sym_os[2]-6*sym_os[1])*u+4*sym_os[8]-4*sym_os[7]-2*sym_os[6]-2*sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]+4*sym_os[6]+2*sym_os[4]-6*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; - A(6,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-4*sym_os[7]-4*sym_os[6]-4*sym_os[5]-4*sym_os[4]+2*sym_os[3]+2*sym_os[2]+2*sym_os[1])*u+4*sym_os[8]+4*sym_os[7]-2*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]-4*sym_os[6]+2*sym_os[4]+2*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; - A(6,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+4*sym_os[7]+12*sym_os[6]-6*sym_os[3]-6*sym_os[2]+2*sym_os[1])*u-4*sym_os[8]-4*sym_os[7]+6*sym_os[6]-2*sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]+4*sym_os[6]+2*sym_os[4]-2*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; - A(6,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-12*sym_os[7]-12*sym_os[6]+4*sym_os[5]+4*sym_os[4]+18*sym_os[3]-6*sym_os[2]-6*sym_os[1])*u-4*sym_os[8]+4*sym_os[7]+6*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]-4*sym_os[6]+2*sym_os[4]+6*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; - A(7,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u)*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[3])+2*sym_os[2]+2*sym_os[1])*u)*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u)/8; - A(7,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2]+6*sym_os[1])*u-2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u+(sym_os[4]-sym_os[5])*u)/8; - A(7,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u+3*sym_os[5]-3*sym_os[4])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]+6*sym_os[2]+2*sym_os[1])*u-sym_os[5]+sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+2*sym_os[3]-2*sym_os[2])*u)/8; - A(7,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+2*sym_os[3]+2*sym_os[2]-2*sym_os[1])*u-2*sym_os[6]+sym_os[5]+sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+(sym_os[4]-sym_os[5])*u*u+(sym_os[4]-sym_os[5])*u)/8; - A(7,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u-sym_os[5]+sym_os[4])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+2*sym_os[3]-2*sym_os[2]+2*sym_os[1])*u-sym_os[5]+sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]-2*sym_os[3]+2*sym_os[2])*u)/8; - A(7,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+12*sym_os[7]+12*sym_os[6]-4*sym_os[5]-4*sym_os[4]-18*sym_os[3]+6*sym_os[2]+6*sym_os[1])*u+4*sym_os[8]-4*sym_os[7]-6*sym_os[6]+2*sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]-4*sym_os[6]+2*sym_os[4]+6*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; - A(7,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-4*sym_os[7]-12*sym_os[6]+6*sym_os[3]+6*sym_os[2]-2*sym_os[1])*u+4*sym_os[8]+4*sym_os[7]-6*sym_os[6]+2*sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]+4*sym_os[6]+2*sym_os[4]-2*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; - A(7,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+4*sym_os[7]+4*sym_os[6]+4*sym_os[5]+4*sym_os[4]-2*sym_os[3]-2*sym_os[2]-2*sym_os[1])*u-4*sym_os[8]-4*sym_os[7]+2*sym_os[6]+2*sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]-4*sym_os[6]+2*sym_os[4]+2*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; - A(7,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-12*sym_os[7]-4*sym_os[6]+6*sym_os[3]-2*sym_os[2]+6*sym_os[1])*u-4*sym_os[8]+4*sym_os[7]+2*sym_os[6]+2*sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]+4*sym_os[6]+2*sym_os[4]-6*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; - A(8,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u)*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[3]-2*sym_os[2]-2*sym_os[1])*u)*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u)/8; - A(8,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2]+2*sym_os[1])*u-2*sym_os[6]+sym_os[5]+sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+(sym_os[4]-sym_os[5])*u*u+(sym_os[5]-sym_os[4])*u)/8; - A(8,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u+3*sym_os[5]-3*sym_os[4])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]-6*sym_os[2]-2*sym_os[1])*u-sym_os[5]+sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[3]+2*sym_os[2])*u)/8; - A(8,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]-2*sym_os[2]-6*sym_os[1])*u-2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u+(sym_os[5]-sym_os[4])*u)/8; - A(8,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u-sym_os[5]+sym_os[4])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-2*sym_os[3]+2*sym_os[2]-2*sym_os[1])*u-sym_os[5]+sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[3]-2*sym_os[2])*u)/8; - A(8,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+4*sym_os[7]+12*sym_os[6]-6*sym_os[3]-6*sym_os[2]+2*sym_os[1])*u+4*sym_os[8]+4*sym_os[7]-6*sym_os[6]+2*sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]-4*sym_os[6]-2*sym_os[4]+2*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; - A(8,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-12*sym_os[7]-12*sym_os[6]+4*sym_os[5]+4*sym_os[4]+18*sym_os[3]-6*sym_os[2]-6*sym_os[1])*u+4*sym_os[8]-4*sym_os[7]-6*sym_os[6]+2*sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]+4*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; - A(8,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+12*sym_os[7]+4*sym_os[6]-6*sym_os[3]+2*sym_os[2]-6*sym_os[1])*u-4*sym_os[8]+4*sym_os[7]+2*sym_os[6]+2*sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]-4*sym_os[6]-2*sym_os[4]+6*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; - A(8,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-4*sym_os[7]-4*sym_os[6]-4*sym_os[5]-4*sym_os[4]+2*sym_os[3]+2*sym_os[2]+2*sym_os[1])*u-4*sym_os[8]-4*sym_os[7]+2*sym_os[6]+2*sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; + A(0,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+2*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u-2*sym_os[0])/2; + A(0,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+(sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[1]-4*sym_os[4])*u+2*sym_os[4]-2*sym_os[0])/2; + A(0,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u-4*sym_os[4]+4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+2*sym_os[4]-2*sym_os[0])/2; + A(0,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+(sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[4]-4*sym_os[1])*u+2*sym_os[4]-2*sym_os[0])/2; + A(0,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+4*sym_os[4]-4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+2*sym_os[4]-2*sym_os[0])/2; + A(0,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+8*sym_os[7]+8*sym_os[6]-8*sym_os[3])*u+4*sym_os[8]-4*sym_os[6]-4*sym_os[4]+4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[4]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[4]-2*sym_os[0])/2; + A(0,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-8*sym_os[7]-8*sym_os[6]+8*sym_os[3])*u+4*sym_os[8]-4*sym_os[6]-4*sym_os[4]+4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[4]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[4]-2*sym_os[0])/2; + A(0,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+8*sym_os[7]+8*sym_os[6]-8*sym_os[3])*u-4*sym_os[8]+4*sym_os[6]+4*sym_os[4]-4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[4]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[4]-2*sym_os[0])/2; + A(0,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-8*sym_os[7]-8*sym_os[6]+8*sym_os[3])*u-4*sym_os[8]+4*sym_os[6]+4*sym_os[4]-4*sym_os[2])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[4]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[4]-2*sym_os[0])/2; + A(1,0)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5]+sym_os[4])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+(sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[0]-2*sym_os[1])*u)/4; + A(1,1)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+(2*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+((-sym_os[5])-3*sym_os[4]+2*sym_os[1]+2*sym_os[0])*u+sym_os[5]+sym_os[4]+2*sym_os[1])/4; + A(1,2)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+4*sym_os[3]-4*sym_os[2])*u+2*sym_os[5]-2*sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5]+sym_os[4])/4; + A(1,3)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+(4*sym_os[5]-2*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(3*sym_os[5]+sym_os[4]-6*sym_os[1]+2*sym_os[0])*u+sym_os[5]+sym_os[4]-2*sym_os[1])/4; + A(1,4)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-4*sym_os[3]+4*sym_os[2])*u-2*sym_os[5]+2*sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5]+sym_os[4])/4; + A(1,5)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+4*sym_os[7]+8*sym_os[6]+2*sym_os[5]+2*sym_os[4]-4*sym_os[3]-4*sym_os[2])*u+4*sym_os[8]+4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]-4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-2*sym_os[5]-4*sym_os[4]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[4]+2*sym_os[1])/4; + A(1,6)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-12*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2])*u+4*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+3*sym_os[5]-3*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+2*sym_os[5]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[4]-2*sym_os[1])/4; + A(1,7)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+12*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2])*u-4*sym_os[8]+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+3*sym_os[5]-3*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+2*sym_os[5]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[4]-2*sym_os[1])/4; + A(1,8)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-4*sym_os[7]-8*sym_os[6]-2*sym_os[5]-2*sym_os[4]+4*sym_os[3]+4*sym_os[2])*u-4*sym_os[8]-4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]+4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-2*sym_os[5]-4*sym_os[4]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[4]+2*sym_os[1])/4; + A(2,0)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u-2*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u)/4; + A(2,1)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2]+2*sym_os[0])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+4*sym_os[3]-4*sym_os[1])*u+2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+(2*sym_os[5]-2*sym_os[4])*u-sym_os[5]+sym_os[4])/4; + A(2,2)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+2*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u-sym_os[5]-3*sym_os[4]+2*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+sym_os[5]+sym_os[4]+2*sym_os[2])/4; + A(2,3)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2]+2*sym_os[0])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-4*sym_os[3]+4*sym_os[1])*u+2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+(2*sym_os[4]-2*sym_os[5])*u-sym_os[5]+sym_os[4])/4; + A(2,4)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+4*sym_os[5]-2*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+3*sym_os[5]+sym_os[4]-6*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+sym_os[5]+sym_os[4]-2*sym_os[2])/4; + A(2,5)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]+2*sym_os[4]-4*sym_os[3]-4*sym_os[1])*u+4*sym_os[8]-2*sym_os[6]-2*sym_os[5]-4*sym_os[4]+2*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]+4*sym_os[6]+2*sym_os[5]-2*sym_os[4]-4*sym_os[3])*u-2*sym_os[8]-2*sym_os[6]+2*sym_os[4]+2*sym_os[2])/4; + A(2,6)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]-2*sym_os[4]+4*sym_os[3]+4*sym_os[1])*u+4*sym_os[8]-2*sym_os[6]-2*sym_os[5]-4*sym_os[4]+2*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]-4*sym_os[6]-2*sym_os[5]+2*sym_os[4]+4*sym_os[3])*u-2*sym_os[8]-2*sym_os[6]+2*sym_os[4]+2*sym_os[2])/4; + A(2,7)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]+3*sym_os[5]-3*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+8*sym_os[7]+12*sym_os[6]-2*sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[1])*u-4*sym_os[8]+6*sym_os[6]+2*sym_os[5]-6*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-4*sym_os[3])*u-2*sym_os[8]+2*sym_os[6]+2*sym_os[4]-2*sym_os[2])/4; + A(2,8)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]+3*sym_os[5]-3*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-8*sym_os[7]-12*sym_os[6]+2*sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[1])*u-4*sym_os[8]+6*sym_os[6]+2*sym_os[5]-6*sym_os[2]+2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+4*sym_os[3])*u-2*sym_os[8]+2*sym_os[6]+2*sym_os[4]-2*sym_os[2])/4; + A(3,0)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5]+sym_os[4])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+(sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[1]-2*sym_os[0])*u)/4; + A(3,1)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+(4*sym_os[5]-2*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+((-3*sym_os[5])-sym_os[4]+6*sym_os[1]-2*sym_os[0])*u+sym_os[5]+sym_os[4]-2*sym_os[1])/4; + A(3,2)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-4*sym_os[3]+4*sym_os[2])*u+2*sym_os[5]-2*sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5]+sym_os[4])/4; + A(3,3)=((sym_os[5]-sym_os[4])*v*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+(2*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(sym_os[5]+3*sym_os[4]-2*sym_os[1]-2*sym_os[0])*u+sym_os[5]+sym_os[4]+2*sym_os[1])/4; + A(3,4)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+4*sym_os[3]-4*sym_os[2])*u-2*sym_os[5]+2*sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5]+sym_os[4])/4; + A(3,5)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+12*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2])*u+4*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+3*sym_os[5]-3*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-2*sym_os[5]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[4]-2*sym_os[1])/4; + A(3,6)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[4]-2*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-4*sym_os[7]-8*sym_os[6]-2*sym_os[5]-2*sym_os[4]+4*sym_os[3]+4*sym_os[2])*u+4*sym_os[8]+4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]-4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+2*sym_os[5]+4*sym_os[4]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[4]+2*sym_os[1])/4; + A(3,7)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+4*sym_os[7]+8*sym_os[6]+2*sym_os[5]+2*sym_os[4]-4*sym_os[3]-4*sym_os[2])*u-4*sym_os[8]-4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]+4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-sym_os[5]+sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+2*sym_os[5]+4*sym_os[4]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[4]+2*sym_os[1])/4; + A(3,8)=((sym_os[5]-sym_os[4])*v*v*v*v+(2*sym_os[5]-2*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-12*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2])*u-4*sym_os[8]+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-4*sym_os[3])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+3*sym_os[5]-3*sym_os[4]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-2*sym_os[5]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[4]-2*sym_os[1])/4; + A(4,0)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+2*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u)/4; + A(4,1)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2]+2*sym_os[0])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-4*sym_os[3]+4*sym_os[1])*u-2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+(2*sym_os[5]-2*sym_os[4])*u-sym_os[5]+sym_os[4])/4; + A(4,2)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+4*sym_os[5]-2*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u-3*sym_os[5]-sym_os[4]+6*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+sym_os[5]+sym_os[4]-2*sym_os[2])/4; + A(4,3)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-4*sym_os[2]+2*sym_os[0])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+4*sym_os[3]-4*sym_os[1])*u-2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+(2*sym_os[4]-2*sym_os[5])*u-sym_os[5]+sym_os[4])/4; + A(4,4)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+2*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+sym_os[5]+3*sym_os[4]-2*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+sym_os[5]+sym_os[4]+2*sym_os[2])/4; + A(4,5)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]+3*sym_os[5]-3*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+8*sym_os[7]+12*sym_os[6]-2*sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[1])*u+4*sym_os[8]-6*sym_os[6]-2*sym_os[5]+6*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+4*sym_os[3])*u-2*sym_os[8]+2*sym_os[6]+2*sym_os[4]-2*sym_os[2])/4; + A(4,6)=((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]+3*sym_os[5]-3*sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-8*sym_os[7]-12*sym_os[6]+2*sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[1])*u+4*sym_os[8]-6*sym_os[6]-2*sym_os[5]+6*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-4*sym_os[3])*u-2*sym_os[8]+2*sym_os[6]+2*sym_os[4]-2*sym_os[2])/4; + A(4,7)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]+2*sym_os[4]-4*sym_os[3]-4*sym_os[1])*u-4*sym_os[8]+2*sym_os[6]+2*sym_os[5]+4*sym_os[4]-2*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[5]-2*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]-4*sym_os[6]-2*sym_os[5]+2*sym_os[4]+4*sym_os[3])*u-2*sym_os[8]-2*sym_os[6]+2*sym_os[4]+2*sym_os[2])/4; + A(4,8)=((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u-2*sym_os[8]+4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[2]+2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]-2*sym_os[4]+4*sym_os[3]+4*sym_os[1])*u-4*sym_os[8]+2*sym_os[6]+2*sym_os[5]+4*sym_os[4]-2*sym_os[2]-2*sym_os[0])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(2*sym_os[4]-2*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]+4*sym_os[6]+2*sym_os[5]-2*sym_os[4]-4*sym_os[3])*u-2*sym_os[8]-2*sym_os[6]+2*sym_os[4]+2*sym_os[2])/4; + A(5,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[3])+2*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u)/8; + A(5,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+2*sym_os[3]+2*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[6]-sym_os[5]-sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+(sym_os[4]-sym_os[5])*u*u+(sym_os[5]-sym_os[4])*u)/8; + A(5,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5]+sym_os[4])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+2*sym_os[3]-2*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u+sym_os[5]-sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[3]-2*sym_os[2])*u)/8; + A(5,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u+(sym_os[5]-sym_os[4])*u)/8; + A(5,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u+3*sym_os[5]-3*sym_os[4])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]+6*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u+sym_os[5]-sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[3]+2*sym_os[2])*u)/8; + A(5,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+4*sym_os[7]+4*sym_os[6]+4*sym_os[5]+4*sym_os[4]-2*sym_os[3]-2*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+4*sym_os[8]+4*sym_os[7]-2*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; + A(5,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-12*sym_os[7]-4*sym_os[6]+6*sym_os[3]-2*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+4*sym_os[8]-4*sym_os[7]-2*sym_os[6]-2*sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]-4*sym_os[6]-2*sym_os[4]+6*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; + A(5,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+12*sym_os[7]+12*sym_os[6]-4*sym_os[5]-4*sym_os[4]-18*sym_os[3]+6*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-4*sym_os[8]+4*sym_os[7]+6*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]+4*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; + A(5,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-4*sym_os[7]-12*sym_os[6]+6*sym_os[3]+6*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-4*sym_os[8]-4*sym_os[7]+6*sym_os[6]-2*sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]-4*sym_os[6]-2*sym_os[4]+2*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; + A(6,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[3]-2*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u)/8; + A(6,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]-2*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u+(sym_os[4]-sym_os[5])*u)/8; + A(6,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5]+sym_os[4])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-2*sym_os[3]+2*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u+sym_os[5]-sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]-2*sym_os[3]+2*sym_os[2])*u)/8; + A(6,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[6]-sym_os[5]-sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+(sym_os[4]-sym_os[5])*u*u+(sym_os[4]-sym_os[5])*u)/8; + A(6,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u+3*sym_os[5]-3*sym_os[4])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]-6*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u+sym_os[5]-sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+2*sym_os[3]-2*sym_os[2])*u)/8; + A(6,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+12*sym_os[7]+4*sym_os[6]-6*sym_os[3]+2*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+4*sym_os[8]-4*sym_os[7]-2*sym_os[6]-2*sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]+4*sym_os[6]+2*sym_os[4]-6*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; + A(6,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-4*sym_os[7]-4*sym_os[6]-4*sym_os[5]-4*sym_os[4]+2*sym_os[3]+2*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+4*sym_os[8]+4*sym_os[7]-2*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]-4*sym_os[6]+2*sym_os[4]+2*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; + A(6,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+4*sym_os[7]+12*sym_os[6]-6*sym_os[3]-6*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-4*sym_os[8]-4*sym_os[7]+6*sym_os[6]-2*sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]+4*sym_os[6]+2*sym_os[4]-2*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; + A(6,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[5]-3*sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-12*sym_os[7]-12*sym_os[6]+4*sym_os[5]+4*sym_os[4]+18*sym_os[3]-6*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-4*sym_os[8]+4*sym_os[7]+6*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]-4*sym_os[6]+2*sym_os[4]+6*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; + A(7,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[3])+2*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u)/8; + A(7,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u+(sym_os[4]-sym_os[5])*u)/8; + A(7,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u+3*sym_os[5]-3*sym_os[4])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]+6*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5]+sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+2*sym_os[3]-2*sym_os[2])*u)/8; + A(7,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+2*sym_os[3]+2*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[6]+sym_os[5]+sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+(sym_os[4]-sym_os[5])*u*u+(sym_os[4]-sym_os[5])*u)/8; + A(7,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5]+sym_os[4])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+2*sym_os[3]-2*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5]+sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-2*sym_os[7])+sym_os[5]+sym_os[4]-2*sym_os[3]+2*sym_os[2])*u)/8; + A(7,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+12*sym_os[7]+12*sym_os[6]-4*sym_os[5]-4*sym_os[4]-18*sym_os[3]+6*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+4*sym_os[8]-4*sym_os[7]-6*sym_os[6]+2*sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]-4*sym_os[6]+2*sym_os[4]+6*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; + A(7,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-4*sym_os[7]-12*sym_os[6]+6*sym_os[3]+6*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+4*sym_os[8]+4*sym_os[7]-6*sym_os[6]+2*sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]+4*sym_os[6]+2*sym_os[4]-2*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; + A(7,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+4*sym_os[7]+4*sym_os[6]+4*sym_os[5]+4*sym_os[4]-2*sym_os[3]-2*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-4*sym_os[8]-4*sym_os[7]+2*sym_os[6]+2*sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]-4*sym_os[6]+2*sym_os[4]+2*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; + A(7,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-12*sym_os[7]-4*sym_os[6]+6*sym_os[3]-2*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-4*sym_os[8]+4*sym_os[7]+2*sym_os[6]+2*sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[4]-3*sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]+4*sym_os[6]+2*sym_os[4]-6*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; + A(8,0)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[3]-2*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u)/8; + A(8,1)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[6]+sym_os[5]+sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+(sym_os[4]-sym_os[5])*u*u+(sym_os[5]-sym_os[4])*u)/8; + A(8,2)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u+3*sym_os[5]-3*sym_os[4])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[7])+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]-6*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5]+sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[3]+2*sym_os[2])*u)/8; + A(8,3)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[4]-sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]-2*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u+(sym_os[5]-sym_os[4])*u)/8; + A(8,4)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5]+sym_os[4])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[7]-2*sym_os[5]-2*sym_os[4]-2*sym_os[3]+2*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5]+sym_os[4])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[5]-sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[3]-2*sym_os[2])*u)/8; + A(8,5)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+4*sym_os[7]+12*sym_os[6]-6*sym_os[3]-6*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+4*sym_os[8]+4*sym_os[7]-6*sym_os[6]+2*sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]-4*sym_os[6]-2*sym_os[4]+2*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; + A(8,6)=-((sym_os[5]-sym_os[4])*v*v*v*v+(3*sym_os[4]-3*sym_os[5])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]+3*sym_os[5]+3*sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-12*sym_os[7]-12*sym_os[6]+4*sym_os[5]+4*sym_os[4]+18*sym_os[3]-6*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+4*sym_os[8]-4*sym_os[7]-6*sym_os[6]+2*sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]+2*sym_os[6]+2*sym_os[5]-4*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]+4*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; + A(8,7)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]-3*sym_os[5]-3*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]+2*sym_os[7]+4*sym_os[6]-2*sym_os[5]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+12*sym_os[7]+4*sym_os[6]-6*sym_os[3]+2*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-4*sym_os[8]+4*sym_os[7]+2*sym_os[6]+2*sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(3*sym_os[5]-3*sym_os[4])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]+2*sym_os[5]-4*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]-4*sym_os[6]-2*sym_os[4]+6*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]+2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; + A(8,8)=-((sym_os[5]-sym_os[4])*v*v*v*v+(sym_os[5]-sym_os[4])*v*v*v+(((-2*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]-2*sym_os[4]-8*sym_os[3]+4*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-4*sym_os[7]-4*sym_os[6]-4*sym_os[5]-4*sym_os[4]+2*sym_os[3]+2*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-4*sym_os[8]-4*sym_os[7]+2*sym_os[6]+2*sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+(sym_os[5]-sym_os[4])*u*u*u*u+(sym_os[4]-sym_os[5])*u*u*u+((-2*sym_os[8])+4*sym_os[7]-2*sym_os[6]-2*sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]+4*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2])*u-2*sym_os[8]-2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; break; default: printf("Error: matrix A not implemented for Q%d and CLBM1\n",Q); } -// cout << "matA CLBM1: "<< A<<endl; } void LBM::setA_CLBM2(matrix &A, int Q, ex u, ex v, ex w) @@ -520,140 +531,146 @@ void LBM::setA_CLBM2(matrix &A, int Q, ex u, ex v, ex w) A(4,4) = n1o4*(sym_os[4]+sym_os[3]-4*sym_os[2]+2*sym_os[0])*v*v+n1o4*(2*sym_os[4]+2*sym_os[3]-2*sym_os[2]-2*sym_os[0])*v+n1o4*(sym_os[3]-sym_os[4])*u*u+n1o4*sym_os[4]+n1o4*sym_os[3]+n1o2*sym_os[2]; break; case 7: - A(0,0) = (2*sym_os[3]-sym_os[4])*w*w+(2*sym_os[2]-sym_os[4])*v*v+(2*sym_os[1]-sym_os[4])*u*u; - A(0,1) = (2*sym_os[3]-sym_os[4])*w*w+(2*sym_os[2]-sym_os[4])*v*v+(2*sym_os[1]-sym_os[4])*u*u+(2*sym_os[4]-2*sym_os[1])*u-sym_os[4]; - A(0,2) = (2*sym_os[3]-sym_os[4])*w*w+(2*sym_os[2]-sym_os[4])*v*v+(2*sym_os[4]-2*sym_os[2])*v+(2*sym_os[1]-sym_os[4])*u*u-sym_os[4]; - A(0,3) = (2*sym_os[3]-sym_os[4])*w*w+(2*sym_os[4]-2*sym_os[3])*w+(2*sym_os[2]-sym_os[4])*v*v+(2*sym_os[1]-sym_os[4])*u*u-sym_os[4]; - A(0,4) = (2*sym_os[3]-sym_os[4])*w*w+(2*sym_os[2]-sym_os[4])*v*v+(2*sym_os[1]-sym_os[4])*u*u+(2*sym_os[1]-2*sym_os[4])*u-sym_os[4]; - A(0,5) = (2*sym_os[3]-sym_os[4])*w*w+(2*sym_os[2]-sym_os[4])*v*v+(2*sym_os[2]-2*sym_os[4])*v+(2*sym_os[1]-sym_os[4])*u*u-sym_os[4]; - A(0,6) = (2*sym_os[3]-sym_os[4])*w*w+(2*sym_os[3]-2*sym_os[4])*w+(2*sym_os[2]-sym_os[4])*v*v+(2*sym_os[1]-sym_os[4])*u*u-sym_os[4]; - A(1,0) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o2*sym_os[1]*u; - A(1,1) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o6*(2*sym_os[6]+2*sym_os[5]+2*sym_os[4]-3*sym_os[1])*u+n1o6*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]+n1o2*sym_os[1]; - A(1,2) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(2*sym_os[4]-2*sym_os[5])*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o2*sym_os[1]*u-n1o6*sym_os[5]+n1o6*sym_os[4]; - A(1,3) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(2*sym_os[4]-2*sym_os[6])*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o2*sym_os[1]*u-n1o6*sym_os[6]+n1o6*sym_os[4]; - A(1,4) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o6*(-2*sym_os[6]-2*sym_os[5]-2*sym_os[4]+9*sym_os[1])*u+n1o6*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]-n1o2*sym_os[1]; - A(1,5) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(2*sym_os[5]-2*sym_os[4])*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o2*sym_os[1]*u-n1o6*sym_os[5]+n1o6*sym_os[4]; - A(1,6) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(2*sym_os[6]-2*sym_os[4])*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o2*sym_os[1]*u-n1o6*sym_os[6]+n1o6*sym_os[4]; - A(2,0) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u; - A(2,1) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-n1o6*(2*sym_os[6]-4*sym_os[5]+2*sym_os[4])*u+n1o6*sym_os[6]-n1o3*sym_os[5]+n1o6*sym_os[4]; - A(2,2) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o6*(4*sym_os[5]+2*sym_os[4]-3*sym_os[2])*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+n1o3*sym_os[5]+n1o6*sym_os[4]+n1o2*sym_os[2]; - A(2,3) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(2*sym_os[4]-2*sym_os[6])*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-n1o6*sym_os[6]+n1o6*sym_os[4]; - A(2,4) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-n1o6*(-2*sym_os[6]+4*sym_os[5]-2*sym_os[4])*u+n1o6*sym_os[6]-n1o3*sym_os[5]+n1o6*sym_os[4]; - A(2,5) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o6*(-4*sym_os[5]-2*sym_os[4]+9*sym_os[2])*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+n1o3*sym_os[5]+n1o6*sym_os[4]-n1o2*sym_os[2]; - A(2,6) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(2*sym_os[6]-2*sym_os[4])*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-n1o6*sym_os[6]+n1o6*sym_os[4]; - A(3,0) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w-n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u; - A(3,1) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w-n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+n1o6*(4*sym_os[6]-2*sym_os[5]-2*sym_os[4])*u-n1o3*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]; - A(3,2) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w-n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(2*sym_os[5]-2*sym_os[4])*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u-n1o6*sym_os[5]+n1o6*sym_os[4]; - A(3,3) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o6*(-4*sym_os[6]-2*sym_os[4]+3*sym_os[3])*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+n1o3*sym_os[6]+n1o6*sym_os[4]+n1o2*sym_os[3]; - A(3,4) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w-n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+n1o6*(-4*sym_os[6]+2*sym_os[5]+2*sym_os[4])*u-n1o3*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]; - A(3,5) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w-n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(2*sym_os[4]-2*sym_os[5])*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u-n1o6*sym_os[5]+n1o6*sym_os[4]; - A(3,6) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o6*(4*sym_os[6]+2*sym_os[4]-9*sym_os[3])*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+n1o3*sym_os[6]+n1o6*sym_os[4]-n1o2*sym_os[3]; - A(4,0) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u+n1o2*sym_os[1]*u; - A(4,1) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o6*(2*sym_os[6]+2*sym_os[5]+2*sym_os[4]-9*sym_os[1])*u+n1o6*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]-n1o2*sym_os[1]; - A(4,2) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(2*sym_os[4]-2*sym_os[5])*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u+n1o2*sym_os[1]*u-n1o6*sym_os[5]+n1o6*sym_os[4]; - A(4,3) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(2*sym_os[4]-2*sym_os[6])*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u+n1o2*sym_os[1]*u-n1o6*sym_os[6]+n1o6*sym_os[4]; - A(4,4) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u-n1o6*(-2*sym_os[6]-2*sym_os[5]-2*sym_os[4]+3*sym_os[1])*u+n1o6*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]+n1o2*sym_os[1]; - A(4,5) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(2*sym_os[5]-2*sym_os[4])*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u+n1o2*sym_os[1]*u-n1o6*sym_os[5]+n1o6*sym_os[4]; - A(4,6) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(2*sym_os[6]-2*sym_os[4])*w-n1o6*(sym_os[5]-sym_os[4])*v*v-n1o6*(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1])*u*u+n1o2*sym_os[1]*u-n1o6*sym_os[6]+n1o6*sym_os[4]; - A(5,0) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v+n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u; - A(5,1) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v+n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-n1o6*(2*sym_os[6]-4*sym_os[5]+2*sym_os[4])*u+n1o6*sym_os[6]-n1o3*sym_os[5]+n1o6*sym_os[4]; - A(5,2) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o6*(4*sym_os[5]+2*sym_os[4]-9*sym_os[2])*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+n1o3*sym_os[5]+n1o6*sym_os[4]-n1o2*sym_os[2]; - A(5,3) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(2*sym_os[4]-2*sym_os[6])*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v+n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-n1o6*sym_os[6]+n1o6*sym_os[4]; - A(5,4) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v+n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-n1o6*(-2*sym_os[6]+4*sym_os[5]-2*sym_os[4])*u+n1o6*sym_os[6]-n1o3*sym_os[5]+n1o6*sym_os[4]; - A(5,5) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v-n1o6*(-4*sym_os[5]-2*sym_os[4]+3*sym_os[2])*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+n1o3*sym_os[5]+n1o6*sym_os[4]+n1o2*sym_os[2]; - A(5,6) = -n1o6*(sym_os[6]-sym_os[4])*w*w-n1o6*(2*sym_os[6]-2*sym_os[4])*w-n1o6*(-2*sym_os[5]-sym_os[4]+6*sym_os[2])*v*v+n1o2*sym_os[2]*v-n1o6*(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-n1o6*sym_os[6]+n1o6*sym_os[4]; - A(6,0) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u; - A(6,1) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+n1o6*(4*sym_os[6]-2*sym_os[5]-2*sym_os[4])*u-n1o3*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]; - A(6,2) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(2*sym_os[5]-2*sym_os[4])*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u-n1o6*sym_os[5]+n1o6*sym_os[4]; - A(6,3) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o6*(-4*sym_os[6]-2*sym_os[4]+9*sym_os[3])*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+n1o3*sym_os[6]+n1o6*sym_os[4]-n1o2*sym_os[3]; - A(6,4) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+n1o6*(-4*sym_os[6]+2*sym_os[5]+2*sym_os[4])*u-n1o3*sym_os[6]+n1o6*sym_os[5]+n1o6*sym_os[4]; - A(6,5) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o2*sym_os[3]*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(2*sym_os[4]-2*sym_os[5])*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u-n1o6*sym_os[5]+n1o6*sym_os[4]; - A(6,6) = n1o6*(2*sym_os[6]+sym_os[4]-6*sym_os[3])*w*w+n1o6*(4*sym_os[6]+2*sym_os[4]-3*sym_os[3])*w+n1o6*(sym_os[4]-sym_os[5])*v*v+n1o6*(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+n1o3*sym_os[6]+n1o6*sym_os[4]+n1o2*sym_os[3]; + A(0,0) = (-sym_os[4]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[4]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u+sym_os[0]; + A(0,1) = (-sym_os[4]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[4]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u+(2*sym_os[4]-2*sym_os[1])*u-sym_os[4]+sym_os[0]; + A(0,2) = (-sym_os[4]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[4]+2*sym_os[2]-sym_os[0])*v*v+(2*sym_os[4]-2*sym_os[2])*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u-sym_os[4]+sym_os[0]; + A(0,3) = (-sym_os[4]+2*sym_os[3]-sym_os[0])*w*w+(2*sym_os[4]-2*sym_os[3])*w+(-sym_os[4]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u-sym_os[4]+sym_os[0]; + A(0,4) = (-sym_os[4]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[4]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u+(2*sym_os[1]-2*sym_os[4])*u-sym_os[4]+sym_os[0]; + A(0,5) = (-sym_os[4]+2*sym_os[3]-sym_os[0])*w*w+(-sym_os[4]+2*sym_os[2]-sym_os[0])*v*v+(2*sym_os[2]-2*sym_os[4])*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u-sym_os[4]+sym_os[0]; + A(0,6) = (-sym_os[4]+2*sym_os[3]-sym_os[0])*w*w+(2*sym_os[3]-2*sym_os[4])*w+(-sym_os[4]+2*sym_os[2]-sym_os[0])*v*v+(-sym_os[4]+2*sym_os[1]-sym_os[0])*u*u-sym_os[4]+sym_os[0]; + + A(1,0) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[1]-3*sym_os[0])*u)/6; + A(1,1) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(2*sym_os[6]+2*sym_os[5]+2*sym_os[4]-3*sym_os[1]-3*sym_os[0])*u-sym_os[6]-sym_os[5]-sym_os[4]-3*sym_os[1])/6; + A(1,2) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(2*sym_os[4]-2*sym_os[5])*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[1]-3*sym_os[0])*u+sym_os[5]-sym_os[4])/6; + A(1,3) = -((sym_os[6]-sym_os[4])*w*w+(2*sym_os[4]-2*sym_os[6])*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[1]-3*sym_os[0])*u+sym_os[6]-sym_os[4])/6; + A(1,4) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(-2*sym_os[6]-2*sym_os[5]-2*sym_os[4]+9*sym_os[1]-3*sym_os[0])*u-sym_os[6]-sym_os[5]-sym_os[4]+3*sym_os[1])/6; + A(1,5) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(2*sym_os[5]-2*sym_os[4])*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[1]-3*sym_os[0])*u+sym_os[5]-sym_os[4])/6; + A(1,6) = -((sym_os[6]-sym_os[4])*w*w+(2*sym_os[6]-2*sym_os[4])*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[1]-3*sym_os[0])*u+sym_os[6]-sym_os[4])/6; + + A(2,0) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[2]-3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u)/6; + A(2,1) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[2]-3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+(2*sym_os[6]-4*sym_os[5]+2*sym_os[4])*u-sym_os[6]+2*sym_os[5]-sym_os[4])/6; + A(2,2) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(4*sym_os[5]+2*sym_os[4]-3*sym_os[2]-3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-2*sym_os[5]-sym_os[4]-3*sym_os[2])/6; + A(2,3) = -((sym_os[6]-sym_os[4])*w*w+(2*sym_os[4]-2*sym_os[6])*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[2]-3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+sym_os[6]-sym_os[4])/6; + A(2,4) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[2]-3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+(-2*sym_os[6]+4*sym_os[5]-2*sym_os[4])*u-sym_os[6]+2*sym_os[5]-sym_os[4])/6; + A(2,5) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(-4*sym_os[5]-2*sym_os[4]+9*sym_os[2]-3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-2*sym_os[5]-sym_os[4]+3*sym_os[2])/6; + A(2,6) = -((sym_os[6]-sym_os[4])*w*w+(2*sym_os[6]-2*sym_os[4])*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[2]-3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+sym_os[6]-sym_os[4])/6; + + A(3,0) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[0]-3*sym_os[3])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u)/6; + A(3,1) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[0]-3*sym_os[3])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4])*u-2*sym_os[6]+sym_os[5]+sym_os[4])/6; + A(3,2) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[0]-3*sym_os[3])*w+(sym_os[4]-sym_os[5])*v*v+(2*sym_os[5]-2*sym_os[4])*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u-sym_os[5]+sym_os[4])/6; + A(3,3) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(-4*sym_os[6]-2*sym_os[4]+3*sym_os[3]+3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+2*sym_os[6]+sym_os[4]+3*sym_os[3])/6; + A(3,4) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[0]-3*sym_os[3])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+(-4*sym_os[6]+2*sym_os[5]+2*sym_os[4])*u-2*sym_os[6]+sym_os[5]+sym_os[4])/6; + A(3,5) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[0]-3*sym_os[3])*w+(sym_os[4]-sym_os[5])*v*v+(2*sym_os[4]-2*sym_os[5])*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u-sym_os[5]+sym_os[4])/6; + A(3,6) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(4*sym_os[6]+2*sym_os[4]-9*sym_os[3]+3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+2*sym_os[6]+sym_os[4]-3*sym_os[3])/6; + + A(4,0) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[0]-3*sym_os[1])*u)/6; + A(4,1) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(2*sym_os[6]+2*sym_os[5]+2*sym_os[4]-9*sym_os[1]+3*sym_os[0])*u-sym_os[6]-sym_os[5]-sym_os[4]+3*sym_os[1])/6; + A(4,2) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(2*sym_os[4]-2*sym_os[5])*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[0]-3*sym_os[1])*u+sym_os[5]-sym_os[4])/6; + A(4,3) = -((sym_os[6]-sym_os[4])*w*w+(2*sym_os[4]-2*sym_os[6])*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[0]-3*sym_os[1])*u+sym_os[6]-sym_os[4])/6; + A(4,4) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(-2*sym_os[6]-2*sym_os[5]-2*sym_os[4]+3*sym_os[1]+3*sym_os[0])*u-sym_os[6]-sym_os[5]-sym_os[4]-3*sym_os[1])/6; + A(4,5) = -((sym_os[6]-sym_os[4])*w*w+(sym_os[5]-sym_os[4])*v*v+(2*sym_os[5]-2*sym_os[4])*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[0]-3*sym_os[1])*u+sym_os[5]-sym_os[4])/6; + A(4,6) = -((sym_os[6]-sym_os[4])*w*w+(2*sym_os[6]-2*sym_os[4])*w+(sym_os[5]-sym_os[4])*v*v+(-sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[1]-3*sym_os[0])*u*u+(3*sym_os[0]-3*sym_os[1])*u+sym_os[6]-sym_os[4])/6; + + A(5,0) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[0]-3*sym_os[2])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u)/6; + A(5,1) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[0]-3*sym_os[2])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+(2*sym_os[6]-4*sym_os[5]+2*sym_os[4])*u-sym_os[6]+2*sym_os[5]-sym_os[4])/6; + A(5,2) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(4*sym_os[5]+2*sym_os[4]-9*sym_os[2]+3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-2*sym_os[5]-sym_os[4]+3*sym_os[2])/6; + A(5,3) = -((sym_os[6]-sym_os[4])*w*w+(2*sym_os[4]-2*sym_os[6])*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[0]-3*sym_os[2])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+sym_os[6]-sym_os[4])/6; + A(5,4) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[0]-3*sym_os[2])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+(-2*sym_os[6]+4*sym_os[5]-2*sym_os[4])*u-sym_os[6]+2*sym_os[5]-sym_os[4])/6; + A(5,5) = -((sym_os[6]-sym_os[4])*w*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(-4*sym_os[5]-2*sym_os[4]+3*sym_os[2]+3*sym_os[0])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u-2*sym_os[5]-sym_os[4]-3*sym_os[2])/6; + A(5,6) = -((sym_os[6]-sym_os[4])*w*w+(2*sym_os[6]-2*sym_os[4])*w+(-2*sym_os[5]-sym_os[4]+6*sym_os[2]-3*sym_os[0])*v*v+(3*sym_os[0]-3*sym_os[2])*v+(-sym_os[6]+2*sym_os[5]-sym_os[4])*u*u+sym_os[6]-sym_os[4])/6; + + A(6,0) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[3]-3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u)/6; + A(6,1) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[3]-3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+(4*sym_os[6]-2*sym_os[5]-2*sym_os[4])*u-2*sym_os[6]+sym_os[5]+sym_os[4])/6; + A(6,2) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[3]-3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(2*sym_os[5]-2*sym_os[4])*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u-sym_os[5]+sym_os[4])/6; + A(6,3) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(-4*sym_os[6]-2*sym_os[4]+9*sym_os[3]-3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+2*sym_os[6]+sym_os[4]-3*sym_os[3])/6; + A(6,4) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[3]-3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+(-4*sym_os[6]+2*sym_os[5]+2*sym_os[4])*u-2*sym_os[6]+sym_os[5]+sym_os[4])/6; + A(6,5) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(3*sym_os[3]-3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(2*sym_os[4]-2*sym_os[5])*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u-sym_os[5]+sym_os[4])/6; + A(6,6) = ((2*sym_os[6]+sym_os[4]-6*sym_os[3]+3*sym_os[0])*w*w+(4*sym_os[6]+2*sym_os[4]-3*sym_os[3]-3*sym_os[0])*w+(sym_os[4]-sym_os[5])*v*v+(-2*sym_os[6]+sym_os[5]+sym_os[4])*u*u+2*sym_os[6]+sym_os[4]+3*sym_os[3])/6; break; case 9: - A(0,0)=(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+4*sym_os[2])*v*v+sym_os[4]*u*u*u*u+(4*sym_os[1]-2*sym_os[4])*u*u)/2; - A(0,1)=(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2])*v*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(4*sym_os[1]-sym_os[4])*u*u+(4*sym_os[4]-4*sym_os[1])*u-2*sym_os[4])/2; - A(0,2)=(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+sym_os[5]+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u-4*sym_os[2])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1])*u*u)/2; - A(0,3)=(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2])*v*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(4*sym_os[1]-sym_os[4])*u*u+(4*sym_os[1]-4*sym_os[4])*u-2*sym_os[4])/2; - A(0,4)=(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+sym_os[5]+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+4*sym_os[2])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1])*u*u)/2; - A(0,5)=(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-8*sym_os[7]-8*sym_os[6]+8*sym_os[3])*u-4*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[4]-4*sym_os[1])*u+2*sym_os[8]-2*sym_os[4])/2; - A(0,6)=(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+8*sym_os[7]+8*sym_os[6]-8*sym_os[3])*u-4*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[4]+4*sym_os[1])*u+2*sym_os[8]-2*sym_os[4])/2; - A(0,7)=(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-8*sym_os[7]-8*sym_os[6]+8*sym_os[3])*u+4*sym_os[8]-4*sym_os[6]+4*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[4]+4*sym_os[1])*u+2*sym_os[8]-2*sym_os[4])/2; - A(0,8)=(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+8*sym_os[7]+8*sym_os[6]-8*sym_os[3])*u+4*sym_os[8]-4*sym_os[6]+4*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[4]-4*sym_os[1])*u+2*sym_os[8]-2*sym_os[4])/2; - A(1,0)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u-sym_os[5])*v*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(4*sym_os[1]-sym_os[4])*u*u+2*sym_os[1]*u)/4; - A(1,1)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(4*sym_os[1]-2*sym_os[4])*u*u+(3*sym_os[4]-2*sym_os[1])*u-sym_os[4]-2*sym_os[1])/4; - A(1,2)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u)*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+(4*sym_os[7]+2*sym_os[5]-4*sym_os[3]+4*sym_os[2])*u+2*sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+2*sym_os[1])*u-sym_os[5])/4; - A(1,3)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[4]+4*sym_os[1])*u*u+(6*sym_os[1]-sym_os[4])*u-sym_os[4]+2*sym_os[1])/4; - A(1,4)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u)*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+((-4*sym_os[7])-2*sym_os[5]+4*sym_os[3]-4*sym_os[2])*u-2*sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+2*sym_os[1])*u-sym_os[5])/4; - A(1,5)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+4*sym_os[3]+4*sym_os[2])*u-4*sym_os[8]-4*sym_os[7]+4*sym_os[6]+2*sym_os[5]+4*sym_os[3])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]-sym_os[5]+3*sym_os[4]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])/4; - A(1,6)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+12*sym_os[7]+8*sym_os[6]+2*sym_os[5]-12*sym_os[3]+4*sym_os[2])*u-4*sym_os[8]+4*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[3])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]+2*sym_os[4]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-sym_os[5]-sym_os[4]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[1])/4; - A(1,7)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-12*sym_os[7]-8*sym_os[6]-2*sym_os[5]+12*sym_os[3]-4*sym_os[2])*u+4*sym_os[8]-4*sym_os[7]-4*sym_os[6]-2*sym_os[5]+4*sym_os[3])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]+2*sym_os[4]+4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-sym_os[5]-sym_os[4]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[1])/4; - A(1,8)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-4*sym_os[3]-4*sym_os[2])*u+4*sym_os[8]+4*sym_os[7]-4*sym_os[6]-2*sym_os[5]-4*sym_os[3])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]-sym_os[5]+3*sym_os[4]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])/4; - A(2,0)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+sym_os[5]+4*sym_os[2])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+2*sym_os[2])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u)/4; - A(2,1)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[4]-4*sym_os[3]+4*sym_os[1])*u-2*sym_os[6]+sym_os[4]+2*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+2*sym_os[4]*u-sym_os[4])/4; - A(2,2)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u-sym_os[5]-2*sym_os[2])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+sym_os[5]-2*sym_os[2])/4; - A(2,3)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[4]+4*sym_os[3]-4*sym_os[1])*u-2*sym_os[6]+sym_os[4]+2*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u-2*sym_os[4]*u-sym_os[4])/4; - A(2,4)=-(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+4*sym_os[5]+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+3*sym_os[5]+6*sym_os[2])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+sym_os[5]+2*sym_os[2])/4; - A(2,5)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[4]+4*sym_os[3]+4*sym_os[1])*u-4*sym_os[8]+2*sym_os[6]-sym_os[5]+sym_os[4]-2*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]-4*sym_os[6]+2*sym_os[4]+4*sym_os[3])*u+2*sym_os[8]+2*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[2])/4; - A(2,6)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[4]-4*sym_os[3]-4*sym_os[1])*u-4*sym_os[8]+2*sym_os[6]-sym_os[5]+sym_os[4]-2*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]+4*sym_os[6]-2*sym_os[4]-4*sym_os[3])*u+2*sym_os[8]+2*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[2])/4; - A(2,7)=-(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+4*sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-8*sym_os[7]-12*sym_os[6]+2*sym_os[4]+12*sym_os[3]-4*sym_os[1])*u+4*sym_os[8]-6*sym_os[6]+3*sym_os[5]+sym_os[4]+6*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[6]-2*sym_os[4]+4*sym_os[3])*u+2*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])/4; - A(2,8)=-(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+4*sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+8*sym_os[7]+12*sym_os[6]-2*sym_os[4]-12*sym_os[3]+4*sym_os[1])*u+4*sym_os[8]-6*sym_os[6]+3*sym_os[5]+sym_os[4]+6*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[6]+2*sym_os[4]-4*sym_os[3])*u+2*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])/4; - A(3,0)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u-sym_os[5])*v*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(4*sym_os[1]-sym_os[4])*u*u-2*sym_os[1]*u)/4; - A(3,1)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[4]+4*sym_os[1])*u*u+(sym_os[4]-6*sym_os[1])*u-sym_os[4]+2*sym_os[1])/4; - A(3,2)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u)*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+((-4*sym_os[7])-2*sym_os[5]+4*sym_os[3]-4*sym_os[2])*u+2*sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-2*sym_os[1])*u-sym_os[5])/4; - A(3,3)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(4*sym_os[1]-2*sym_os[4])*u*u+(2*sym_os[1]-3*sym_os[4])*u-sym_os[4]-2*sym_os[1])/4; - A(3,4)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u)*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+(4*sym_os[7]+2*sym_os[5]-4*sym_os[3]+4*sym_os[2])*u-2*sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-2*sym_os[1])*u-sym_os[5])/4; - A(3,5)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-12*sym_os[7]-8*sym_os[6]-2*sym_os[5]+12*sym_os[3]-4*sym_os[2])*u-4*sym_os[8]+4*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[3])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]+2*sym_os[4]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+sym_os[5]+sym_os[4]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[1])/4; - A(3,6)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-4*sym_os[3]-4*sym_os[2])*u-4*sym_os[8]-4*sym_os[7]+4*sym_os[6]+2*sym_os[5]+4*sym_os[3])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]+sym_os[5]-3*sym_os[4]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])/4; - A(3,7)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+4*sym_os[3]+4*sym_os[2])*u+4*sym_os[8]+4*sym_os[7]-4*sym_os[6]-2*sym_os[5]-4*sym_os[3])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]+sym_os[5]-3*sym_os[4]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])/4; - A(3,8)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+12*sym_os[7]+8*sym_os[6]+2*sym_os[5]-12*sym_os[3]+4*sym_os[2])*u+4*sym_os[8]-4*sym_os[7]-4*sym_os[6]-2*sym_os[5]+4*sym_os[3])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]+2*sym_os[4]+4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+sym_os[5]+sym_os[4]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[1])/4; - A(4,0)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+sym_os[5]+4*sym_os[2])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u-2*sym_os[2])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u)/4; - A(4,1)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[4]+4*sym_os[3]-4*sym_os[1])*u+2*sym_os[6]-sym_os[4]-2*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+2*sym_os[4]*u-sym_os[4])/4; - A(4,2)=-(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+4*sym_os[5]+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u-3*sym_os[5]-6*sym_os[2])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+sym_os[5]+2*sym_os[2])/4; - A(4,3)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[4]-4*sym_os[3]+4*sym_os[1])*u+2*sym_os[6]-sym_os[4]-2*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u-2*sym_os[4]*u-sym_os[4])/4; - A(4,4)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+sym_os[5]+2*sym_os[2])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+sym_os[5]-2*sym_os[2])/4; - A(4,5)=-(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+4*sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-8*sym_os[7]-12*sym_os[6]+2*sym_os[4]+12*sym_os[3]-4*sym_os[1])*u-4*sym_os[8]+6*sym_os[6]-3*sym_os[5]-sym_os[4]-6*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[6]+2*sym_os[4]-4*sym_os[3])*u+2*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])/4; - A(4,6)=-(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+4*sym_os[5]+sym_os[4]+4*sym_os[2])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+8*sym_os[7]+12*sym_os[6]-2*sym_os[4]-12*sym_os[3]+4*sym_os[1])*u-4*sym_os[8]+6*sym_os[6]-3*sym_os[5]-sym_os[4]-6*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[6]-2*sym_os[4]+4*sym_os[3])*u+2*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])/4; - A(4,7)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[4]+4*sym_os[3]+4*sym_os[1])*u+4*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]+4*sym_os[6]-2*sym_os[4]-4*sym_os[3])*u+2*sym_os[8]+2*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[2])/4; - A(4,8)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[4]-4*sym_os[3]-4*sym_os[1])*u+4*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]-4*sym_os[6]+2*sym_os[4]+4*sym_os[3])*u+2*sym_os[8]+2*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[2])/4; - A(5,0)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u)*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[3]-2*sym_os[2]-2*sym_os[1])*u)*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u)/8; - A(5,1)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2]+2*sym_os[1])*u-2*sym_os[6]+sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u-sym_os[4]*u*u+sym_os[4]*u)/8; - A(5,2)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u-sym_os[5])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[7]+2*sym_os[5]-2*sym_os[3]+2*sym_os[2]-2*sym_os[1])*u+sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-2*sym_os[7])-sym_os[5]-2*sym_os[3]+2*sym_os[2])*u)/8; - A(5,3)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[4]+6*sym_os[3]-2*sym_os[2]-6*sym_os[1])*u-2*sym_os[6]+sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+3*sym_os[4]*u*u+sym_os[4]*u)/8; - A(5,4)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u+3*sym_os[5])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[7])-2*sym_os[5]+6*sym_os[3]-6*sym_os[2]-2*sym_os[1])*u+sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-2*sym_os[7])-sym_os[5]+2*sym_os[3]-2*sym_os[2])*u)/8; - A(5,5)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+2*sym_os[3]+2*sym_os[2]+2*sym_os[1])*u-4*sym_os[8]-4*sym_os[7]+2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+2*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; - A(5,6)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+12*sym_os[7]+4*sym_os[6]+2*sym_os[5]+2*sym_os[4]-6*sym_os[3]+2*sym_os[2]-6*sym_os[1])*u-4*sym_os[8]+4*sym_os[7]+2*sym_os[6]+sym_os[5]+sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]+3*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]+4*sym_os[6]-sym_os[5]+sym_os[4]-6*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; - A(5,7)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-12*sym_os[7]-12*sym_os[6]-2*sym_os[5]+2*sym_os[4]+18*sym_os[3]-6*sym_os[2]-6*sym_os[1])*u+4*sym_os[8]-4*sym_os[7]-6*sym_os[6]+sym_os[5]+sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+3*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+6*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; - A(5,8)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+4*sym_os[7]+12*sym_os[6]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]-6*sym_os[2]+2*sym_os[1])*u+4*sym_os[8]+4*sym_os[7]-6*sym_os[6]+sym_os[5]+sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]+4*sym_os[6]-sym_os[5]+sym_os[4]-2*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; - A(6,0)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u)*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[3])+2*sym_os[2]+2*sym_os[1])*u)*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u)/8; - A(6,1)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2]+6*sym_os[1])*u-2*sym_os[6]+sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+3*sym_os[4]*u*u-sym_os[4]*u)/8; - A(6,2)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u-sym_os[5])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[7])-2*sym_os[5]+2*sym_os[3]-2*sym_os[2]+2*sym_os[1])*u+sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(2*sym_os[7]+sym_os[5]+2*sym_os[3]-2*sym_os[2])*u)/8; - A(6,3)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[4]+2*sym_os[3]+2*sym_os[2]-2*sym_os[1])*u-2*sym_os[6]+sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u-sym_os[4]*u*u-sym_os[4]*u)/8; - A(6,4)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u+3*sym_os[5])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[7]+2*sym_os[5]-6*sym_os[3]+6*sym_os[2]+2*sym_os[1])*u+sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(2*sym_os[7]+sym_os[5]-2*sym_os[3]+2*sym_os[2])*u)/8; - A(6,5)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-12*sym_os[7]-4*sym_os[6]-2*sym_os[5]-2*sym_os[4]+6*sym_os[3]-2*sym_os[2]+6*sym_os[1])*u-4*sym_os[8]+4*sym_os[7]+2*sym_os[6]+sym_os[5]+sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]+3*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]-4*sym_os[6]+sym_os[5]-sym_os[4]+6*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; - A(6,6)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-2*sym_os[3]-2*sym_os[2]-2*sym_os[1])*u-4*sym_os[8]-4*sym_os[7]+2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]+4*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; - A(6,7)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+(8*sym_os[8]-4*sym_os[7]-12*sym_os[6]+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]+6*sym_os[2]-2*sym_os[1])*u+4*sym_os[8]+4*sym_os[7]-6*sym_os[6]+sym_os[5]+sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; - A(6,8)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1])*u*u+((-8*sym_os[8])+12*sym_os[7]+12*sym_os[6]+2*sym_os[5]-2*sym_os[4]-18*sym_os[3]+6*sym_os[2]+6*sym_os[1])*u+4*sym_os[8]-4*sym_os[7]-6*sym_os[6]+sym_os[5]+sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+3*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]+4*sym_os[6]+sym_os[5]-sym_os[4]-6*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; - A(7,0)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u)*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+(2*sym_os[3]-2*sym_os[2]-2*sym_os[1])*u)*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u)/8; - A(7,1)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[4]+6*sym_os[3]-2*sym_os[2]-6*sym_os[1])*u+2*sym_os[6]-sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+3*sym_os[4]*u*u-sym_os[4]*u)/8; - A(7,2)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u+3*sym_os[5])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[7])-2*sym_os[5]+6*sym_os[3]-6*sym_os[2]-2*sym_os[1])*u-sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(2*sym_os[7]+sym_os[5]-2*sym_os[3]+2*sym_os[2])*u)/8; - A(7,3)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2]+2*sym_os[1])*u+2*sym_os[6]-sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u-sym_os[4]*u*u-sym_os[4]*u)/8; - A(7,4)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1])*u-sym_os[5])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[7]+2*sym_os[5]-2*sym_os[3]+2*sym_os[2]-2*sym_os[1])*u-sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(2*sym_os[7]+sym_os[5]+2*sym_os[3]-2*sym_os[2])*u)/8; - A(7,5)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-12*sym_os[7]-12*sym_os[6]-2*sym_os[5]+2*sym_os[4]+18*sym_os[3]-6*sym_os[2]-6*sym_os[1])*u-4*sym_os[8]+4*sym_os[7]+6*sym_os[6]-sym_os[5]-sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+3*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]+4*sym_os[6]+sym_os[5]-sym_os[4]-6*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; - A(7,6)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+4*sym_os[7]+12*sym_os[6]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]-6*sym_os[2]+2*sym_os[1])*u-4*sym_os[8]-4*sym_os[7]+6*sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; - A(7,7)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+2*sym_os[3]+2*sym_os[2]+2*sym_os[1])*u+4*sym_os[8]+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]+4*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; - A(7,8)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+12*sym_os[7]+4*sym_os[6]+2*sym_os[5]+2*sym_os[4]-6*sym_os[3]+2*sym_os[2]-6*sym_os[1])*u+4*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]+3*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]-4*sym_os[6]+sym_os[5]-sym_os[4]+6*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; - A(8,0)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u)*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+((-2*sym_os[3])+2*sym_os[2]+2*sym_os[1])*u)*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u)/8; - A(8,1)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[6])+2*sym_os[4]+2*sym_os[3]+2*sym_os[2]-2*sym_os[1])*u+2*sym_os[6]-sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u-sym_os[4]*u*u+sym_os[4]*u)/8; - A(8,2)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u+3*sym_os[5])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[7]+2*sym_os[5]-6*sym_os[3]+6*sym_os[2]+2*sym_os[1])*u-sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-2*sym_os[7])-sym_os[5]+2*sym_os[3]-2*sym_os[2])*u)/8; - A(8,3)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1])*u*u+(4*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2]+6*sym_os[1])*u+2*sym_os[6]-sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+3*sym_os[4]*u*u+sym_os[4]*u)/8; - A(8,4)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1])*u-sym_os[5])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+((-4*sym_os[7])-2*sym_os[5]+2*sym_os[3]-2*sym_os[2]+2*sym_os[1])*u-sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-2*sym_os[7])-sym_os[5]-2*sym_os[3]+2*sym_os[2])*u)/8; - A(8,5)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-4*sym_os[7]-12*sym_os[6]+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]+6*sym_os[2]-2*sym_os[1])*u-4*sym_os[8]-4*sym_os[7]+6*sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]+4*sym_os[6]-sym_os[5]+sym_os[4]-2*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; - A(8,6)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+12*sym_os[7]+12*sym_os[6]+2*sym_os[5]-2*sym_os[4]-18*sym_os[3]+6*sym_os[2]+6*sym_os[1])*u-4*sym_os[8]+4*sym_os[7]+6*sym_os[6]-sym_os[5]-sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+3*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+6*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; - A(8,7)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+(8*sym_os[8]-12*sym_os[7]-4*sym_os[6]-2*sym_os[5]-2*sym_os[4]+6*sym_os[3]-2*sym_os[2]+6*sym_os[1])*u+4*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]+3*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]+4*sym_os[6]-sym_os[5]+sym_os[4]-6*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; - A(8,8)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1])*u*u+((-8*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-2*sym_os[3]-2*sym_os[2]-2*sym_os[1])*u+4*sym_os[8]+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+2*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; - break; - default: + A(0,0)=(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+4*sym_os[2]-2*sym_os[0])*v*v+sym_os[4]*u*u*u*u+((-2*sym_os[4])+4*sym_os[1]-2*sym_os[0])*u*u+2*sym_os[0])/2; + A(0,1)=(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+((-sym_os[4])+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[4]-4*sym_os[1])*u-2*sym_os[4]+2*sym_os[0])/2; + A(0,2)=(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+sym_os[5]+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u-4*sym_os[2])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+2*sym_os[0])/2; + A(0,3)=(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+((-sym_os[4])+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[1]-4*sym_os[4])*u-2*sym_os[4]+2*sym_os[0])/2; + A(0,4)=(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+sym_os[5]+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+4*sym_os[2])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+2*sym_os[0])/2; + A(0,5)=(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-8*sym_os[7]-8*sym_os[6]+8*sym_os[3])*u-4*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[4]-4*sym_os[1])*u+2*sym_os[8]-2*sym_os[4]+2*sym_os[0])/2; + A(0,6)=(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+8*sym_os[7]+8*sym_os[6]-8*sym_os[3])*u-4*sym_os[8]+4*sym_os[6]-4*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[4]+4*sym_os[1])*u+2*sym_os[8]-2*sym_os[4]+2*sym_os[0])/2; + A(0,7)=(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-8*sym_os[7]-8*sym_os[6]+8*sym_os[3])*u+4*sym_os[8]-4*sym_os[6]+4*sym_os[2])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[4]+4*sym_os[1])*u+2*sym_os[8]-2*sym_os[4]+2*sym_os[0])/2; + A(0,8)=(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+8*sym_os[7]+8*sym_os[6]-8*sym_os[3])*u+4*sym_os[8]-4*sym_os[6]+4*sym_os[2])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[4]-4*sym_os[1])*u+2*sym_os[8]-2*sym_os[4]+2*sym_os[0])/2; + A(1,0)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5])*v*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+((-sym_os[4])+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[1]-2*sym_os[0])*u)/4; + A(1,1)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+((-2*sym_os[4])+4*sym_os[1]-2*sym_os[0])*u*u+(3*sym_os[4]-2*sym_os[1]-2*sym_os[0])*u-sym_os[4]-2*sym_os[1])/4; + A(1,2)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+(4*sym_os[7]+2*sym_os[5]-4*sym_os[3]+4*sym_os[2])*u+2*sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5])/4; + A(1,3)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-sym_os[4])+6*sym_os[1]-2*sym_os[0])*u-sym_os[4]+2*sym_os[1])/4; + A(1,4)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+((-4*sym_os[7])-2*sym_os[5]+4*sym_os[3]-4*sym_os[2])*u-2*sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5])/4; + A(1,5)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+4*sym_os[3]+4*sym_os[2])*u-4*sym_os[8]-4*sym_os[7]+4*sym_os[6]+2*sym_os[5]+4*sym_os[3])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]-sym_os[5]+3*sym_os[4]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])/4; + A(1,6)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+12*sym_os[7]+8*sym_os[6]+2*sym_os[5]-12*sym_os[3]+4*sym_os[2])*u-4*sym_os[8]+4*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[3])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]+2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-sym_os[5]-sym_os[4]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[1])/4; + A(1,7)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-12*sym_os[7]-8*sym_os[6]-2*sym_os[5]+12*sym_os[3]-4*sym_os[2])*u+4*sym_os[8]-4*sym_os[7]-4*sym_os[6]-2*sym_os[5]+4*sym_os[3])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]+2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-sym_os[5]-sym_os[4]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[1])/4; + A(1,8)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-4*sym_os[3]-4*sym_os[2])*u+4*sym_os[8]+4*sym_os[7]-4*sym_os[6]-2*sym_os[5]-4*sym_os[3])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]-sym_os[5]+3*sym_os[4]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])/4; + A(2,0)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+sym_os[5]+4*sym_os[2]-2*sym_os[0])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+2*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u)/4; + A(2,1)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[4]-4*sym_os[3]+4*sym_os[1])*u-2*sym_os[6]+sym_os[4]+2*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+2*sym_os[4]*u-sym_os[4])/4; + A(2,2)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u-sym_os[5]-2*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+sym_os[5]-2*sym_os[2])/4; + A(2,3)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[4]+4*sym_os[3]-4*sym_os[1])*u-2*sym_os[6]+sym_os[4]+2*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u-2*sym_os[4]*u-sym_os[4])/4; + A(2,4)=-(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+4*sym_os[5]+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+3*sym_os[5]+6*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+sym_os[5]+2*sym_os[2])/4; + A(2,5)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[4]+4*sym_os[3]+4*sym_os[1])*u-4*sym_os[8]+2*sym_os[6]-sym_os[5]+sym_os[4]-2*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]-4*sym_os[6]+2*sym_os[4]+4*sym_os[3])*u+2*sym_os[8]+2*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[2])/4; + A(2,6)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[4]-4*sym_os[3]-4*sym_os[1])*u-4*sym_os[8]+2*sym_os[6]-sym_os[5]+sym_os[4]-2*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]+4*sym_os[6]-2*sym_os[4]-4*sym_os[3])*u+2*sym_os[8]+2*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[2])/4; + A(2,7)=-(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+4*sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-8*sym_os[7]-12*sym_os[6]+2*sym_os[4]+12*sym_os[3]-4*sym_os[1])*u+4*sym_os[8]-6*sym_os[6]+3*sym_os[5]+sym_os[4]+6*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[6]-2*sym_os[4]+4*sym_os[3])*u+2*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])/4; + A(2,8)=-(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+4*sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+8*sym_os[7]+12*sym_os[6]-2*sym_os[4]-12*sym_os[3]+4*sym_os[1])*u+4*sym_os[8]-6*sym_os[6]+3*sym_os[5]+sym_os[4]+6*sym_os[2]-2*sym_os[0])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[6]+2*sym_os[4]-4*sym_os[3])*u+2*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])/4; + A(3,0)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5])*v*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+((-sym_os[4])+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[0]-2*sym_os[1])*u)/4; + A(3,1)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(sym_os[4]-6*sym_os[1]+2*sym_os[0])*u-sym_os[4]+2*sym_os[1])/4; + A(3,2)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+((-4*sym_os[7])-2*sym_os[5]+4*sym_os[3]-4*sym_os[2])*u+2*sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5])/4; + A(3,3)=-(sym_os[5]*v*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+((-2*sym_os[4])+4*sym_os[1]-2*sym_os[0])*u*u+((-3*sym_os[4])+2*sym_os[1]+2*sym_os[0])*u-sym_os[4]-2*sym_os[1])/4; + A(3,4)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+(4*sym_os[7]+2*sym_os[5]-4*sym_os[3]+4*sym_os[2])*u-2*sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5])/4; + A(3,5)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+(8*sym_os[8]-12*sym_os[7]-8*sym_os[6]-2*sym_os[5]+12*sym_os[3]-4*sym_os[2])*u-4*sym_os[8]+4*sym_os[7]+4*sym_os[6]+2*sym_os[5]-4*sym_os[3])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]+2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+sym_os[5]+sym_os[4]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[1])/4; + A(3,6)=-(sym_os[5]*v*v*v*v-2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[5]-8*sym_os[3]+4*sym_os[2])*u*u+((-8*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[5]-4*sym_os[3]-4*sym_os[2])*u-4*sym_os[8]-4*sym_os[7]+4*sym_os[6]+2*sym_os[5]+4*sym_os[3])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]+sym_os[5]-3*sym_os[4]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])/4; + A(3,7)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+(8*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[5]+4*sym_os[3]+4*sym_os[2])*u+4*sym_os[8]+4*sym_os[7]-4*sym_os[6]-2*sym_os[5]-4*sym_os[3])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]-2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]+sym_os[5]-3*sym_os[4]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-sym_os[5]-sym_os[4]-2*sym_os[1])/4; + A(3,8)=-(sym_os[5]*v*v*v*v+2*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[5]+8*sym_os[3]-4*sym_os[2])*u*u+((-8*sym_os[8])+12*sym_os[7]+8*sym_os[6]+2*sym_os[5]-12*sym_os[3]+4*sym_os[2])*u+4*sym_os[8]-4*sym_os[7]-4*sym_os[6]-2*sym_os[5]+4*sym_os[3])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-sym_os[5]+2*sym_os[4]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+sym_os[5]+sym_os[4]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-sym_os[5]-sym_os[4]+2*sym_os[1])/4; + A(4,0)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+sym_os[5]+4*sym_os[2]-2*sym_os[0])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u-2*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u)/4; + A(4,1)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[4]+4*sym_os[3]-4*sym_os[1])*u+2*sym_os[6]-sym_os[4]-2*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+2*sym_os[4]*u-sym_os[4])/4; + A(4,2)=-(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+4*sym_os[5]+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u-3*sym_os[5]-6*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+sym_os[5]+2*sym_os[2])/4; + A(4,3)=-(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[4]-4*sym_os[3]+4*sym_os[1])*u+2*sym_os[6]-sym_os[4]-2*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u-2*sym_os[4]*u-sym_os[4])/4; + A(4,4)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+sym_os[5]+2*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+sym_os[5]-2*sym_os[2])/4; + A(4,5)=-(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+4*sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-8*sym_os[7]-12*sym_os[6]+2*sym_os[4]+12*sym_os[3]-4*sym_os[1])*u-4*sym_os[8]+6*sym_os[6]-3*sym_os[5]-sym_os[4]-6*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]+4*sym_os[6]+2*sym_os[4]-4*sym_os[3])*u+2*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])/4; + A(4,6)=-(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+4*sym_os[5]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+8*sym_os[7]+12*sym_os[6]-2*sym_os[4]-12*sym_os[3]+4*sym_os[1])*u-4*sym_os[8]+6*sym_os[6]-3*sym_os[5]-sym_os[4]-6*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]-4*sym_os[6]-2*sym_os[4]+4*sym_os[3])*u+2*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2])/4; + A(4,7)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-4*sym_os[7]-8*sym_os[6]+2*sym_os[4]+8*sym_os[3]-4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-8*sym_os[7]-4*sym_os[6]-2*sym_os[4]+4*sym_os[3]+4*sym_os[1])*u+4*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u+2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-4*sym_os[7]+4*sym_os[6]-2*sym_os[4]-4*sym_os[3])*u+2*sym_os[8]+2*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[2])/4; + A(4,8)=-(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+4*sym_os[7]+8*sym_os[6]-2*sym_os[4]-8*sym_os[3]+4*sym_os[1])*u+2*sym_os[8]-4*sym_os[6]+sym_os[4]+4*sym_os[2]-2*sym_os[0])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+8*sym_os[7]+4*sym_os[6]+2*sym_os[4]-4*sym_os[3]-4*sym_os[1])*u+4*sym_os[8]-2*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[2]+2*sym_os[0])*v+sym_os[4]*u*u*u*u-2*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+4*sym_os[7]-4*sym_os[6]+2*sym_os[4]+4*sym_os[3])*u+2*sym_os[8]+2*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[2])/4; + A(5,0)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[3]-2*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u)/8; + A(5,1)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-2*sym_os[6]+sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u-sym_os[4]*u*u+sym_os[4]*u)/8; + A(5,2)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[7]+2*sym_os[5]-2*sym_os[3]+2*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u+sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-2*sym_os[7])-sym_os[5]-2*sym_os[3]+2*sym_os[2])*u)/8; + A(5,3)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[4]+6*sym_os[3]-2*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-2*sym_os[6]+sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+3*sym_os[4]*u*u+sym_os[4]*u)/8; + A(5,4)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u+3*sym_os[5])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[7])-2*sym_os[5]+6*sym_os[3]-6*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u+sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-2*sym_os[7])-sym_os[5]+2*sym_os[3]-2*sym_os[2])*u)/8; + A(5,5)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+2*sym_os[3]+2*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-4*sym_os[8]-4*sym_os[7]+2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+2*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; + A(5,6)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+12*sym_os[7]+4*sym_os[6]+2*sym_os[5]+2*sym_os[4]-6*sym_os[3]+2*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-4*sym_os[8]+4*sym_os[7]+2*sym_os[6]+sym_os[5]+sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]+3*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]+4*sym_os[6]-sym_os[5]+sym_os[4]-6*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; + A(5,7)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-12*sym_os[7]-12*sym_os[6]-2*sym_os[5]+2*sym_os[4]+18*sym_os[3]-6*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+4*sym_os[8]-4*sym_os[7]-6*sym_os[6]+sym_os[5]+sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+3*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+6*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; + A(5,8)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+4*sym_os[7]+12*sym_os[6]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]-6*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+4*sym_os[8]+4*sym_os[7]-6*sym_os[6]+sym_os[5]+sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]+4*sym_os[6]-sym_os[5]+sym_os[4]-2*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; + A(6,0)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[3])+2*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u)/8; + A(6,1)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-2*sym_os[6]+sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+3*sym_os[4]*u*u-sym_os[4]*u)/8; + A(6,2)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[7])-2*sym_os[5]+2*sym_os[3]-2*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u+sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(2*sym_os[7]+sym_os[5]+2*sym_os[3]-2*sym_os[2])*u)/8; + A(6,3)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-2*sym_os[6])+sym_os[4]+4*sym_os[3]-2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[4]+2*sym_os[3]+2*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-2*sym_os[6]+sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u-sym_os[4]*u*u-sym_os[4]*u)/8; + A(6,4)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u+3*sym_os[5])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[7]+2*sym_os[5]-6*sym_os[3]+6*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u+sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(2*sym_os[7]+sym_os[5]-2*sym_os[3]+2*sym_os[2])*u)/8; + A(6,5)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-12*sym_os[7]-4*sym_os[6]-2*sym_os[5]-2*sym_os[4]+6*sym_os[3]-2*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-4*sym_os[8]+4*sym_os[7]+2*sym_os[6]+sym_os[5]+sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]+3*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]-4*sym_os[6]+sym_os[5]-sym_os[4]+6*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; + A(6,6)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+2*sym_os[6]+2*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-2*sym_os[3]-2*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-4*sym_os[8]-4*sym_os[7]+2*sym_os[6]+sym_os[5]+sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]+4*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; + A(6,7)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(8*sym_os[8]-4*sym_os[7]-12*sym_os[6]+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]+6*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+4*sym_os[8]+4*sym_os[7]-6*sym_os[6]+sym_os[5]+sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; + A(6,8)=(sym_os[5]*v*v*v*v+3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-6*sym_os[6]-2*sym_os[5]+sym_os[4]+12*sym_os[3]-6*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-8*sym_os[8])+12*sym_os[7]+12*sym_os[6]+2*sym_os[5]-2*sym_os[4]-18*sym_os[3]+6*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+4*sym_os[8]-4*sym_os[7]-6*sym_os[6]+sym_os[5]+sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+3*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]+4*sym_os[6]+sym_os[5]-sym_os[4]-6*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; + A(7,0)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(2*sym_os[3]-2*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u)/8; + A(7,1)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[4]+6*sym_os[3]-2*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[6]-sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+3*sym_os[4]*u*u-sym_os[4]*u)/8; + A(7,2)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u+3*sym_os[5])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[7])-2*sym_os[5]+6*sym_os[3]-6*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+(2*sym_os[7]+sym_os[5]-2*sym_os[3]+2*sym_os[2])*u)/8; + A(7,3)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[4]-2*sym_os[3]-2*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[6]-sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u-sym_os[4]*u*u-sym_os[4]*u)/8; + A(7,4)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(2*sym_os[7]+sym_os[5]-4*sym_os[3]+4*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[7]+2*sym_os[5]-2*sym_os[3]+2*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+(2*sym_os[7]+sym_os[5]+2*sym_os[3]-2*sym_os[2])*u)/8; + A(7,5)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-12*sym_os[7]-12*sym_os[6]-2*sym_os[5]+2*sym_os[4]+18*sym_os[3]-6*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u-4*sym_os[8]+4*sym_os[7]+6*sym_os[6]-sym_os[5]-sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+3*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]+4*sym_os[6]+sym_os[5]-sym_os[4]-6*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; + A(7,6)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+4*sym_os[7]+12*sym_os[6]-2*sym_os[5]-2*sym_os[4]-6*sym_os[3]-6*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u-4*sym_os[8]-4*sym_os[7]+6*sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[5]-sym_os[4]+2*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; + A(7,7)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-2*sym_os[7]-8*sym_os[6]+sym_os[5]+2*sym_os[4]+4*sym_os[3]+4*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-4*sym_os[7]-4*sym_os[6]+2*sym_os[5]-2*sym_os[4]+2*sym_os[3]+2*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+4*sym_os[8]+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-2*sym_os[7]+4*sym_os[6]+sym_os[5]-sym_os[4]-2*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; + A(7,8)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+6*sym_os[7]+8*sym_os[6]+sym_os[5]-2*sym_os[4]-12*sym_os[3]+4*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+12*sym_os[7]+4*sym_os[6]+2*sym_os[5]+2*sym_os[4]-6*sym_os[3]+2*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+4*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u-3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]+3*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+6*sym_os[7]-4*sym_os[6]+sym_os[5]-sym_os[4]+6*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; + A(8,0)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u)*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-2*sym_os[3])+2*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u)*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u)/8; + A(8,1)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[6])+2*sym_os[4]+2*sym_os[3]+2*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+2*sym_os[6]-sym_os[4]+2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u-sym_os[4]*u*u+sym_os[4]*u)/8; + A(8,2)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u+3*sym_os[5])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[7]+2*sym_os[5]-6*sym_os[3]+6*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+4*sym_os[3]-2*sym_os[2])*u*u+((-2*sym_os[7])-sym_os[5]+2*sym_os[3]-2*sym_os[2])*u)/8; + A(8,3)=(sym_os[5]*v*v*v*v-sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((2*sym_os[6]-sym_os[4]-4*sym_os[3]+2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(4*sym_os[6]-2*sym_os[4]-6*sym_os[3]+2*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+2*sym_os[6]-sym_os[4]-2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+3*sym_os[4]*u*u+sym_os[4]*u)/8; + A(8,4)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-2*sym_os[7])-sym_os[5]+4*sym_os[3]-4*sym_os[2]-2*sym_os[1]+2*sym_os[0])*u-sym_os[5])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-4*sym_os[7])-2*sym_os[5]+2*sym_os[3]-2*sym_os[2]+2*sym_os[1]-2*sym_os[0])*u-sym_os[5])*v+sym_os[4]*u*u*u*u+sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-4*sym_os[3]+2*sym_os[2])*u*u+((-2*sym_os[7])-sym_os[5]-2*sym_os[3]+2*sym_os[2])*u)/8; + A(8,5)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-4*sym_os[7]-12*sym_os[6]+2*sym_os[5]+2*sym_os[4]+6*sym_os[3]+6*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u-4*sym_os[8]-4*sym_os[7]+6*sym_os[6]-sym_os[5]-sym_os[4]+6*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]+4*sym_os[6]-sym_os[5]+sym_os[4]-2*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]-2*sym_os[6]-2*sym_os[3])/8; + A(8,6)=(sym_os[5]*v*v*v*v-3*sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]+3*sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+(((-4*sym_os[8])+8*sym_os[7]+6*sym_os[6]+2*sym_os[5]-sym_os[4]-12*sym_os[3]+6*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+12*sym_os[7]+12*sym_os[6]+2*sym_os[5]-2*sym_os[4]-18*sym_os[3]+6*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u-4*sym_os[8]+4*sym_os[7]+6*sym_os[6]-sym_os[5]-sym_os[4]-6*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]+3*sym_os[4]+4*sym_os[3]-2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+6*sym_os[3]-2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]-2*sym_os[6]+2*sym_os[3])/8; + A(8,7)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+(4*sym_os[8]-6*sym_os[7]-8*sym_os[6]-sym_os[5]+2*sym_os[4]+12*sym_os[3]-4*sym_os[2]-6*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]-2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+4*sym_os[3]-2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+(8*sym_os[8]-12*sym_os[7]-4*sym_os[6]-2*sym_os[5]-2*sym_os[4]+6*sym_os[3]-2*sym_os[2]+6*sym_os[1]-2*sym_os[0])*u+4*sym_os[8]-4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]+2*sym_os[3]+2*sym_os[1])*v+sym_os[4]*u*u*u*u+3*sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]+3*sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+(4*sym_os[8]-6*sym_os[7]+4*sym_os[6]-sym_os[5]+sym_os[4]-6*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]-2*sym_os[7]+2*sym_os[6]-2*sym_os[3])/8; + A(8,8)=(sym_os[5]*v*v*v*v+sym_os[5]*v*v*v+((2*sym_os[8]-4*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+8*sym_os[3]-4*sym_os[2]-4*sym_os[1]+2*sym_os[0])*u*u+((-4*sym_os[8])+2*sym_os[7]+8*sym_os[6]-sym_os[5]-2*sym_os[4]-4*sym_os[3]-4*sym_os[2]+2*sym_os[1]+2*sym_os[0])*u+2*sym_os[8]+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]-4*sym_os[3]+2*sym_os[1])*v*v+((4*sym_os[8]-8*sym_os[7]-2*sym_os[6]-2*sym_os[5]-sym_os[4]+4*sym_os[3]-2*sym_os[2]+4*sym_os[1]-2*sym_os[0])*u*u+((-8*sym_os[8])+4*sym_os[7]+4*sym_os[6]-2*sym_os[5]+2*sym_os[4]-2*sym_os[3]-2*sym_os[2]-2*sym_os[1]-2*sym_os[0])*u+4*sym_os[8]+4*sym_os[7]-2*sym_os[6]-sym_os[5]-sym_os[4]-2*sym_os[3]-2*sym_os[1])*v+sym_os[4]*u*u*u*u-sym_os[4]*u*u*u+(2*sym_os[8]-4*sym_os[7]+2*sym_os[6]-sym_os[5]-sym_os[4]-4*sym_os[3]+2*sym_os[2])*u*u+((-4*sym_os[8])+2*sym_os[7]-4*sym_os[6]-sym_os[5]+sym_os[4]+2*sym_os[3]+2*sym_os[2])*u+2*sym_os[8]+2*sym_os[7]+2*sym_os[6]+2*sym_os[3])/8; + break; + default: printf("Error: matrix A not implemented for Q%d and CLBM2\n",Q); } } @@ -692,138 +709,144 @@ void LBM::setA_MRT1_OG(matrix &A, int Q, ex u, ex v, ex w) A(4,4) = n1o6*sym_os[4]+n2o15*sym_os[3]+n1o2*sym_os[2]+n1o5*sym_os[0]; break; case 7: - A(0,0) = n2o3*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]; - A(0,1) = -n1o7*sym_os[4]; - A(0,2) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(0,3) = -n1o3*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]; - A(0,4) = -n1o7*sym_os[4]; - A(0,5) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(0,6) = -n1o3*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]; - A(1,0) = -n1o7*sym_os[4]; - A(1,1) = n5o14*sym_os[4]+n1o2*sym_os[1]; - A(1,2) = -n1o7*sym_os[4]; - A(1,3) = -n1o7*sym_os[4]; - A(1,4) = n5o14*sym_os[4]-n1o2*sym_os[1]; - A(1,5) = -n1o7*sym_os[4]; - A(1,6) = -n1o7*sym_os[4]; - A(2,0) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(2,1) = -n1o7*sym_os[4]; - A(2,2) = n3o10*sym_os[5]+n2o35*sym_os[4]+n1o2*sym_os[2]; - A(2,3) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(2,4) = -n1o7*sym_os[4]; - A(2,5) = n3o10*sym_os[5]+n2o35*sym_os[4]-n1o2*sym_os[2]; - A(2,6) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(3,0) = -n1o3*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]; - A(3,1) = -n1o7*sym_os[4]; - A(3,2) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(3,3) = n1o6*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]+n1o2*sym_os[3]; - A(3,4) = -n1o7*sym_os[4]; - A(3,5) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(3,6) = n1o6*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]-n1o2*sym_os[3]; - A(4,0) = -n1o7*sym_os[4]; - A(4,1) = n5o14*sym_os[4]-n1o2*sym_os[1]; - A(4,2) = -n1o7*sym_os[4]; - A(4,3) = -n1o7*sym_os[4]; - A(4,4) = n5o14*sym_os[4]+n1o2*sym_os[1]; - A(4,5) = -n1o7*sym_os[4]; - A(4,6) = -n1o7*sym_os[4]; - A(5,0) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(5,1) = -n1o7*sym_os[4]; - A(5,2) = n3o10*sym_os[5]+n2o35*sym_os[4]-n1o2*sym_os[2]; - A(5,3) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(5,4) = -n1o7*sym_os[4]; - A(5,5) = n3o10*sym_os[5]+n2o35*sym_os[4]+n1o2*sym_os[2]; - A(5,6) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(6,0) = -n1o3*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]; - A(6,1) = -n1o7*sym_os[4]; - A(6,2) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(6,3) = n1o6*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]-n1o2*sym_os[3]; - A(6,4) = -n1o7*sym_os[4]; - A(6,5) = n2o35*sym_os[4]-n1o5*sym_os[5]; - A(6,6) = n1o6*sym_os[6]+n2o15*sym_os[5]+n2o35*sym_os[4]+n1o2*sym_os[3]; + A(0,0) = (2*sym_os[6])/3+(2*sym_os[5])/15+(2*sym_os[4])/35+sym_os[0]/7; + A(0,1) = sym_os[0]/7-sym_os[4]/7; + A(0,2) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(0,3) = -sym_os[6]/3+(2*sym_os[5])/15+(2*sym_os[4])/35+sym_os[0]/7; + A(0,4) = sym_os[0]/7-sym_os[4]/7; + A(0,5) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(0,6) = -sym_os[6]/3+(2*sym_os[5])/15+(2*sym_os[4])/35+sym_os[0]/7; + + A(1,0) = sym_os[0]/7-sym_os[4]/7; + A(1,1) = (5*sym_os[4])/14+sym_os[1]/2+sym_os[0]/7; + A(1,2) = sym_os[0]/7-sym_os[4]/7; + A(1,3) = sym_os[0]/7-sym_os[4]/7; + A(1,4) = (5*sym_os[4])/14-sym_os[1]/2+sym_os[0]/7; + A(1,5) = sym_os[0]/7-sym_os[4]/7; + A(1,6) = sym_os[0]/7-sym_os[4]/7; + + A(2,0) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(2,1) = sym_os[0]/7-sym_os[4]/7; + A(2,2) = (3*sym_os[5])/10+(2*sym_os[4])/35+sym_os[2]/2+sym_os[0]/7; + A(2,3) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(2,4) = sym_os[0]/7-sym_os[4]/7; + A(2,5) = (3*sym_os[5])/10+(2*sym_os[4])/35-sym_os[2]/2+sym_os[0]/7; + A(2,6) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + + A(3,0) = -sym_os[6]/3+(2*sym_os[5])/15+(2*sym_os[4])/35+sym_os[0]/7; + A(3,1) = sym_os[0]/7-sym_os[4]/7; + A(3,2) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(3,3) = sym_os[6]/6+(2*sym_os[5])/15+(2*sym_os[4])/35+sym_os[3]/2+sym_os[0]/7; + A(3,4) = sym_os[0]/7-sym_os[4]/7; + A(3,5) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(3,6) = sym_os[6]/6+(2*sym_os[5])/15+(2*sym_os[4])/35-sym_os[3]/2+sym_os[0]/7; + + A(4,0) = sym_os[0]/7-sym_os[4]/7; + A(4,1) = (5*sym_os[4])/14-sym_os[1]/2+sym_os[0]/7; + A(4,2) = sym_os[0]/7-sym_os[4]/7; + A(4,3) = sym_os[0]/7-sym_os[4]/7; + A(4,4) = (5*sym_os[4])/14+sym_os[1]/2+sym_os[0]/7; + A(4,5) = sym_os[0]/7-sym_os[4]/7; + A(4,6) = sym_os[0]/7-sym_os[4]/7; + + A(5,0) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(5,1) = sym_os[0]/7-sym_os[4]/7; + A(5,2) = (3*sym_os[5])/10+(2*sym_os[4])/35-sym_os[2]/2+sym_os[0]/7; + A(5,3) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(5,4) = sym_os[0]/7-sym_os[4]/7; + A(5,5) = (3*sym_os[5])/10+(2*sym_os[4])/35+sym_os[2]/2+sym_os[0]/7; + A(5,6) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + + A(6,0) = -sym_os[6]/3+(2*sym_os[5])/15+(2*sym_os[4])/35+sym_os[0]/7; + A(6,1) = sym_os[0]/7-sym_os[4]/7; + A(6,2) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(6,3) = sym_os[6]/6+(2*sym_os[5])/15+(2*sym_os[4])/35-sym_os[3]/2+sym_os[0]/7; + A(6,4) = sym_os[0]/7-sym_os[4]/7; + A(6,5) = -sym_os[5]/5+(2*sym_os[4])/35+sym_os[0]/7; + A(6,6) = sym_os[6]/6+(2*sym_os[5])/15+(2*sym_os[4])/35+sym_os[3]/2+sym_os[0]/7; break; case 9: - A(0,0)=(4*sym_os[8])/9+(2*sym_os[5])/9+(2*sym_os[4])/9; - A(0,1)=(-(2*sym_os[8])/9)+(2*sym_os[5])/9-sym_os[4]/9; - A(0,2)=(-(2*sym_os[8])/9)-sym_os[5]/9+(2*sym_os[4])/9; - A(0,3)=(-(2*sym_os[8])/9)+(2*sym_os[5])/9-sym_os[4]/9; - A(0,4)=(-(2*sym_os[8])/9)-sym_os[5]/9+(2*sym_os[4])/9; - A(0,5)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(0,6)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(0,7)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(0,8)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(1,0)=(-(2*sym_os[8])/9)+(2*sym_os[5])/9-sym_os[4]/9; - A(1,1)=sym_os[8]/9+sym_os[7]/3+(2*sym_os[5])/9+sym_os[4]/18+sym_os[1]/6; - A(1,2)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(1,3)=sym_os[8]/9-sym_os[7]/3+(2*sym_os[5])/9+sym_os[4]/18-sym_os[1]/6; - A(1,4)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(1,5)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6; - A(1,6)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6; - A(1,7)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6; - A(1,8)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6; - A(2,0)=(-(2*sym_os[8])/9)-sym_os[5]/9+(2*sym_os[4])/9; - A(2,1)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(2,2)=sym_os[8]/9+sym_os[6]/3+sym_os[5]/18+(2*sym_os[4])/9+sym_os[2]/6; - A(2,3)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(2,4)=sym_os[8]/9-sym_os[6]/3+sym_os[5]/18+(2*sym_os[4])/9-sym_os[2]/6; - A(2,5)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6; - A(2,6)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6; - A(2,7)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6; - A(2,8)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6; - A(3,0)=(-(2*sym_os[8])/9)+(2*sym_os[5])/9-sym_os[4]/9; - A(3,1)=sym_os[8]/9-sym_os[7]/3+(2*sym_os[5])/9+sym_os[4]/18-sym_os[1]/6; - A(3,2)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(3,3)=sym_os[8]/9+sym_os[7]/3+(2*sym_os[5])/9+sym_os[4]/18+sym_os[1]/6; - A(3,4)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(3,5)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6; - A(3,6)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6; - A(3,7)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6; - A(3,8)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6; - A(4,0)=(-(2*sym_os[8])/9)-sym_os[5]/9+(2*sym_os[4])/9; - A(4,1)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(4,2)=sym_os[8]/9-sym_os[6]/3+sym_os[5]/18+(2*sym_os[4])/9-sym_os[2]/6; - A(4,3)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9; - A(4,4)=sym_os[8]/9+sym_os[6]/3+sym_os[5]/18+(2*sym_os[4])/9+sym_os[2]/6; - A(4,5)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6; - A(4,6)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6; - A(4,7)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6; - A(4,8)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6; - A(5,0)=(1*sym_os[8])/9-sym_os[5]/9-sym_os[4]/9; - A(5,1)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6; - A(5,2)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6; - A(5,3)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6; - A(5,4)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6; - A(5,5)=sym_os[8]/36+sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4+sym_os[2]/6+sym_os[1]/6; - A(5,6)=sym_os[8]/36-sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4+sym_os[2]/6-sym_os[1]/6; - A(5,7)=sym_os[8]/36-sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4-sym_os[2]/6-sym_os[1]/6; - A(5,8)=sym_os[8]/36+sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4-sym_os[2]/6+sym_os[1]/6; - A(6,0)=(1*sym_os[8])/9-sym_os[5]/9-sym_os[4]/9; - A(6,1)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6; - A(6,2)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6; - A(6,3)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6; - A(6,4)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6; - A(6,5)=sym_os[8]/36-sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4+sym_os[2]/6-sym_os[1]/6; - A(6,6)=sym_os[8]/36+sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4+sym_os[2]/6+sym_os[1]/6; - A(6,7)=sym_os[8]/36+sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4-sym_os[2]/6+sym_os[1]/6; - A(6,8)=sym_os[8]/36-sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4-sym_os[2]/6-sym_os[1]/6; - A(7,0)=(1*sym_os[8])/9-sym_os[5]/9-sym_os[4]/9; - A(7,1)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6; - A(7,2)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6; - A(7,3)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6; - A(7,4)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6; - A(7,5)=sym_os[8]/36-sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4-sym_os[2]/6-sym_os[1]/6; - A(7,6)=sym_os[8]/36+sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4-sym_os[2]/6+sym_os[1]/6; - A(7,7)=sym_os[8]/36+sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4+sym_os[2]/6+sym_os[1]/6; - A(7,8)=sym_os[8]/36-sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4+sym_os[2]/6-sym_os[1]/6; - A(8,0)=(1*sym_os[8])/9-sym_os[5]/9-sym_os[4]/9; - A(8,1)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6; - A(8,2)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6; - A(8,3)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6; - A(8,4)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6; - A(8,5)=sym_os[8]/36+sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4-sym_os[2]/6+sym_os[1]/6; - A(8,6)=sym_os[8]/36-sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4-sym_os[2]/6-sym_os[1]/6; - A(8,7)=sym_os[8]/36-sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4+sym_os[2]/6-sym_os[1]/6; - A(8,8)=sym_os[8]/36+sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4+sym_os[2]/6+sym_os[1]/6; + A(0,0)=(4*sym_os[8])/9+(2*sym_os[5])/9+(2*sym_os[4])/9+sym_os[0]/9; + A(0,1)=(-(2*sym_os[8])/9)+(2*sym_os[5])/9-sym_os[4]/9+sym_os[0]/9; + A(0,2)=(-(2*sym_os[8])/9)-sym_os[5]/9+(2*sym_os[4])/9+sym_os[0]/9; + A(0,3)=(-(2*sym_os[8])/9)+(2*sym_os[5])/9-sym_os[4]/9+sym_os[0]/9; + A(0,4)=(-(2*sym_os[8])/9)-sym_os[5]/9+(2*sym_os[4])/9+sym_os[0]/9; + A(0,5)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(0,6)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(0,7)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(0,8)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(1,0)=(-(2*sym_os[8])/9)+(2*sym_os[5])/9-sym_os[4]/9+sym_os[0]/9; + A(1,1)=sym_os[8]/9+sym_os[7]/3+(2*sym_os[5])/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(1,2)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(1,3)=sym_os[8]/9-sym_os[7]/3+(2*sym_os[5])/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(1,4)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(1,5)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(1,6)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(1,7)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(1,8)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(2,0)=(-(2*sym_os[8])/9)-sym_os[5]/9+(2*sym_os[4])/9+sym_os[0]/9; + A(2,1)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(2,2)=sym_os[8]/9+sym_os[6]/3+sym_os[5]/18+(2*sym_os[4])/9+sym_os[2]/6+sym_os[0]/9; + A(2,3)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(2,4)=sym_os[8]/9-sym_os[6]/3+sym_os[5]/18+(2*sym_os[4])/9-sym_os[2]/6+sym_os[0]/9; + A(2,5)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6+sym_os[0]/9; + A(2,6)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6+sym_os[0]/9; + A(2,7)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6+sym_os[0]/9; + A(2,8)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6+sym_os[0]/9; + A(3,0)=(-(2*sym_os[8])/9)+(2*sym_os[5])/9-sym_os[4]/9+sym_os[0]/9; + A(3,1)=sym_os[8]/9-sym_os[7]/3+(2*sym_os[5])/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(3,2)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(3,3)=sym_os[8]/9+sym_os[7]/3+(2*sym_os[5])/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(3,4)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(3,5)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(3,6)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(3,7)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(3,8)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(4,0)=(-(2*sym_os[8])/9)-sym_os[5]/9+(2*sym_os[4])/9+sym_os[0]/9; + A(4,1)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(4,2)=sym_os[8]/9-sym_os[6]/3+sym_os[5]/18+(2*sym_os[4])/9-sym_os[2]/6+sym_os[0]/9; + A(4,3)=sym_os[8]/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(4,4)=sym_os[8]/9+sym_os[6]/3+sym_os[5]/18+(2*sym_os[4])/9+sym_os[2]/6+sym_os[0]/9; + A(4,5)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6+sym_os[0]/9; + A(4,6)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6+sym_os[0]/9; + A(4,7)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6+sym_os[0]/9; + A(4,8)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6+sym_os[0]/9; + A(5,0)=(1*sym_os[8])/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(5,1)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(5,2)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6+sym_os[0]/9; + A(5,3)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(5,4)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6+sym_os[0]/9; + A(5,5)=sym_os[8]/36+sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4+sym_os[2]/6+sym_os[1]/6+sym_os[0]/9; + A(5,6)=sym_os[8]/36-sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4+sym_os[2]/6-sym_os[1]/6+sym_os[0]/9; + A(5,7)=sym_os[8]/36-sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4-sym_os[2]/6-sym_os[1]/6+sym_os[0]/9; + A(5,8)=sym_os[8]/36+sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4-sym_os[2]/6+sym_os[1]/6+sym_os[0]/9; + A(6,0)=(1*sym_os[8])/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(6,1)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(6,2)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6+sym_os[0]/9; + A(6,3)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(6,4)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6+sym_os[0]/9; + A(6,5)=sym_os[8]/36-sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4+sym_os[2]/6-sym_os[1]/6+sym_os[0]/9; + A(6,6)=sym_os[8]/36+sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4+sym_os[2]/6+sym_os[1]/6+sym_os[0]/9; + A(6,7)=sym_os[8]/36+sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4-sym_os[2]/6+sym_os[1]/6+sym_os[0]/9; + A(6,8)=sym_os[8]/36-sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4-sym_os[2]/6-sym_os[1]/6+sym_os[0]/9; + A(7,0)=(1*sym_os[8])/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(7,1)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(7,2)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6+sym_os[0]/9; + A(7,3)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(7,4)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6+sym_os[0]/9; + A(7,5)=sym_os[8]/36-sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4-sym_os[2]/6-sym_os[1]/6+sym_os[0]/9; + A(7,6)=sym_os[8]/36+sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4-sym_os[2]/6+sym_os[1]/6+sym_os[0]/9; + A(7,7)=sym_os[8]/36+sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4+sym_os[2]/6+sym_os[1]/6+sym_os[0]/9; + A(7,8)=sym_os[8]/36-sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4+sym_os[2]/6-sym_os[1]/6+sym_os[0]/9; + A(8,0)=(1*sym_os[8])/9-sym_os[5]/9-sym_os[4]/9+sym_os[0]/9; + A(8,1)=(-sym_os[8]/18)-sym_os[7]/6-sym_os[5]/9+sym_os[4]/18+sym_os[1]/6+sym_os[0]/9; + A(8,2)=(-sym_os[8]/18)+sym_os[6]/6+sym_os[5]/18-sym_os[4]/9-sym_os[2]/6+sym_os[0]/9; + A(8,3)=(-sym_os[8]/18)+sym_os[7]/6-sym_os[5]/9+sym_os[4]/18-sym_os[1]/6+sym_os[0]/9; + A(8,4)=(-sym_os[8]/18)-sym_os[6]/6+sym_os[5]/18-sym_os[4]/9+sym_os[2]/6+sym_os[0]/9; + A(8,5)=sym_os[8]/36+sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4-sym_os[2]/6+sym_os[1]/6+sym_os[0]/9; + A(8,6)=sym_os[8]/36-sym_os[7]/12-sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4-sym_os[2]/6-sym_os[1]/6+sym_os[0]/9; + A(8,7)=sym_os[8]/36-sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18-sym_os[3]/4+sym_os[2]/6-sym_os[1]/6+sym_os[0]/9; + A(8,8)=sym_os[8]/36+sym_os[7]/12+sym_os[6]/12+sym_os[5]/18+sym_os[4]/18+sym_os[3]/4+sym_os[2]/6+sym_os[1]/6+sym_os[0]/9; break; default: printf("Error: matrix A not implemented forQ%d and MRT1_OG\n",Q); @@ -863,55 +886,61 @@ void LBM::setA_MRT2_OG(matrix &A, int Q, ex u, ex v, ex w) A(4,4) = n1o4*sym_os[4]+n1o20*sym_os[3]+n1o2*sym_os[2]+n1o5*sym_os[0]; break; case 7: - A(0,0) = n6o7*sym_os[4]; - A(0,1) = -n1o7*sym_os[4]; - A(0,2) = -n1o7*sym_os[4]; - A(0,3) = -n1o7*sym_os[4]; - A(0,4) = -n1o7*sym_os[4]; - A(0,5) = -n1o7*sym_os[4]; - A(0,6) = -n1o7*sym_os[4]; - A(1,0) = -n1o7*sym_os[4]; - A(1,1) = n1o12*sym_os[6]+n1o4*sym_os[5]+n1o42*sym_os[4]+n1o2*sym_os[1]; - A(1,2) = n1o12*sym_os[6]-n1o4*sym_os[5]+n1o42*sym_os[4]; - A(1,3) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(1,4) = n1o12*sym_os[6]+n1o4*sym_os[5]+n1o42*sym_os[4]-n1o2*sym_os[1]; - A(1,5) = n1o12*sym_os[6]-n1o4*sym_os[5]+n1o42*sym_os[4]; - A(1,6) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(2,0) = -n1o7*sym_os[4]; - A(2,1) = n1o12*sym_os[6]-n1o4*sym_os[5]+n1o42*sym_os[4]; - A(2,2) = n1o12*sym_os[6]+n1o4*sym_os[5]+n1o42*sym_os[4]+n1o2*sym_os[2]; - A(2,3) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(2,4) = n1o12*sym_os[6]-n1o4*sym_os[5]+n1o42*sym_os[4]; - A(2,5) = n1o12*sym_os[6]+n1o4*sym_os[5]+n1o42*sym_os[4]-n1o2*sym_os[2]; - A(2,6) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(3,0) = -n1o7*sym_os[4]; - A(3,1) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(3,2) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(3,3) = n1o3*sym_os[6]+n1o42*sym_os[4]+n1o2*sym_os[3]; - A(3,4) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(3,5) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(3,6) = n1o3*sym_os[6]+n1o42*sym_os[4]-n1o2*sym_os[3]; - A(4,0) = -n1o7*sym_os[4]; - A(4,1) = n1o12*sym_os[6]+n1o4*sym_os[5]+n1o42*sym_os[4]-n1o2*sym_os[1]; - A(4,2) = n1o12*sym_os[6]-n1o4*sym_os[5]+n1o42*sym_os[4]; - A(4,3) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(4,4) = n1o12*sym_os[6]+n1o4*sym_os[5]+n1o42*sym_os[4]+n1o2*sym_os[1]; - A(4,5) = n1o12*sym_os[6]-n1o4*sym_os[5]+n1o42*sym_os[4]; - A(4,6) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(5,0) = -n1o7*sym_os[4]; - A(5,1) = n1o12*sym_os[6]-n1o4*sym_os[5]+n1o42*sym_os[4]; - A(5,2) = n1o12*sym_os[6]+n1o4*sym_os[5]+n1o42*sym_os[4]-n1o2*sym_os[2]; - A(5,3) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(5,4) = n1o12*sym_os[6]-n1o4*sym_os[5]+n1o42*sym_os[4]; - A(5,5) = n1o12*sym_os[6]+n1o4*sym_os[5]+n1o42*sym_os[4]+n1o2*sym_os[2]; - A(5,6) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(6,0) = -n1o7*sym_os[4]; - A(6,1) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(6,2) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(6,3) = n1o3*sym_os[6]+n1o42*sym_os[4]-n1o2*sym_os[3]; - A(6,4) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(6,5) = -n1o6*sym_os[6]+n1o42*sym_os[4]; - A(6,6) = n1o3*sym_os[6]+n1o42*sym_os[4]+n1o2*sym_os[3]; + A(0,0) = (6*sym_os[4]+sym_os[0])/7; + A(0,1) = -(sym_os[4]-sym_os[0])/7; + A(0,2) =-(sym_os[4]-sym_os[0])/7; + A(0,3) =-(sym_os[4]-sym_os[0])/7; + A(0,4) =-(sym_os[4]-sym_os[0])/7; + A(0,5) =-(sym_os[4]-sym_os[0])/7; + A(0,6) =-(sym_os[4]-sym_os[0])/7; + + A(1,0) =-(sym_os[4]-sym_os[0])/7; + A(1,1) =(7*sym_os[6]+21*sym_os[5]+2*sym_os[4]+42*sym_os[1]+12*sym_os[0])/84; + A(1,2) =(7*sym_os[6]-21*sym_os[5]+2*sym_os[4]+12*sym_os[0])/84; + A(1,3) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(1,4) =(7*sym_os[6]+21*sym_os[5]+2*sym_os[4]-42*sym_os[1]+12*sym_os[0])/84; + A(1,5) =(7*sym_os[6]-21*sym_os[5]+2*sym_os[4]+12*sym_os[0])/84; + A(1,6) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + + A(2,0) =-(sym_os[4]-sym_os[0])/7; + A(2,1) =(7*sym_os[6]-21*sym_os[5]+2*sym_os[4]+12*sym_os[0])/84; + A(2,2) =(7*sym_os[6]+21*sym_os[5]+2*sym_os[4]+42*sym_os[2]+12*sym_os[0])/84; + A(2,3) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(2,4) =(7*sym_os[6]-21*sym_os[5]+2*sym_os[4]+12*sym_os[0])/84; + A(2,5) =(7*sym_os[6]+21*sym_os[5]+2*sym_os[4]-42*sym_os[2]+12*sym_os[0])/84; + A(2,6) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + + A(3,0) =-(sym_os[4]-sym_os[0])/7; + A(3,1) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(3,2) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(3,3) =(14*sym_os[6]+sym_os[4]+21*sym_os[3]+6*sym_os[0])/42; + A(3,4) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(3,5) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(3,6) =(14*sym_os[6]+sym_os[4]-21*sym_os[3]+6*sym_os[0])/42; + + A(4,0) =-(sym_os[4]-sym_os[0])/7; + A(4,1) =(7*sym_os[6]+21*sym_os[5]+2*sym_os[4]-42*sym_os[1]+12*sym_os[0])/84; + A(4,2) =(7*sym_os[6]-21*sym_os[5]+2*sym_os[4]+12*sym_os[0])/84; + A(4,3) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(4,4) =(7*sym_os[6]+21*sym_os[5]+2*sym_os[4]+42*sym_os[1]+12*sym_os[0])/84; + A(4,5) =(7*sym_os[6]-21*sym_os[5]+2*sym_os[4]+12*sym_os[0])/84; + A(4,6) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + + A(5,0) =-(sym_os[4]-sym_os[0])/7; + A(5,1) =(7*sym_os[6]-21*sym_os[5]+2*sym_os[4]+12*sym_os[0])/84; + A(5,2) =(7*sym_os[6]+21*sym_os[5]+2*sym_os[4]-42*sym_os[2]+12*sym_os[0])/84; + A(5,3) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(5,4) =(7*sym_os[6]-21*sym_os[5]+2*sym_os[4]+12*sym_os[0])/84; + A(5,5) =(7*sym_os[6]+21*sym_os[5]+2*sym_os[4]+42*sym_os[2]+12*sym_os[0])/84; + A(5,6) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + + A(6,0) =-(sym_os[4]-sym_os[0])/7; + A(6,1) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(6,2) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(6,3) =(14*sym_os[6]+sym_os[4]-21*sym_os[3]+6*sym_os[0])/42; + A(6,4) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(6,5) =-(7*sym_os[6]-sym_os[4]-6*sym_os[0])/42; + A(6,6) =(14*sym_os[6]+sym_os[4]+21*sym_os[3]+6*sym_os[0])/42; break; default: printf("Error: matrix A not implemented for Q%d and MRT2_OG\n",Q); @@ -1299,78 +1328,16 @@ void LBM::Feq(matrix &F, ex u, ex v, ex w, ex &sym_cs, int Q, int order) break; default: printf("warning: Feq for Q=%d is not implemented yet!\n",Q); } -// ex sum=0; -// for (int i=0;i<Q;i++) sum += F(i,0); -// cout << "F sum is "<<expand(sum)<<endl; } bool LBM::moment_symbol_number(char *desc, int q, int Q) { - if (q==0) - { - sprintf(desc,""); - return false; - } - else - { - switch (Q) - { - case 5: - if (q==1) sprintf(desc,"10"); - if (q==2) sprintf(desc,"01"); - if (q==3) sprintf(desc,"20"); - if (q==4) sprintf(desc,"02"); - return true; - case 7: - if (q==1) sprintf(desc,"100"); - if (q==2) sprintf(desc,"010"); - if (q==3) sprintf(desc,"001"); - if (q==4) sprintf(desc,"200"); - if (q==5) sprintf(desc,"020"); - if (q==6) sprintf(desc,"002"); - return true; - case 27: - if (q==1) sprintf(desc,"100"); - if (q==2) sprintf(desc,"010"); - if (q==3) sprintf(desc,"001"); - if (q==4) sprintf(desc,"110"); - if (q==5) sprintf(desc,"101"); - if (q==6) sprintf(desc,"011"); - if (q==7) sprintf(desc,"111"); - if (q==8) sprintf(desc,"200"); - if (q==9) sprintf(desc,"020"); - if (q==10) sprintf(desc,"002"); - if (q==11) sprintf(desc,"210"); - if (q==12) sprintf(desc,"201"); - if (q==13) sprintf(desc,"211"); - if (q==14) sprintf(desc,"120"); - if (q==15) sprintf(desc,"021"); - if (q==16) sprintf(desc,"121"); - if (q==17) sprintf(desc,"102"); - if (q==18) sprintf(desc,"012"); - if (q==19) sprintf(desc,"112"); - if (q==20) sprintf(desc,"220"); - if (q==21) sprintf(desc,"202"); - if (q==22) sprintf(desc,"022"); - if (q==23) sprintf(desc,"221"); - if (q==24) sprintf(desc,"212"); - if (q==25) sprintf(desc,"122"); - if (q==26) sprintf(desc,"222"); - return true; - default: - sprintf(desc,"%d",q); - return true; - } - } - return false; + sprintf(desc,"%d",q+1); + return true; } void LBM::moment_symbol(char *desc, int q, int Q) { - if (q==0) - sprintf(desc,"\\phi"); - else - sprintf(desc,"m"); + sprintf(desc,"\\mu"); } - diff --git a/main.cpp b/main.cpp index 513eb3a37f50dafb3b4519bdbbdb20b6ea58013c..eba48b02a34410cf217c7cbd1688e0769f69dd7f 100644 --- a/main.cpp +++ b/main.cpp @@ -29,22 +29,20 @@ #include "defs.h" #include "core.h" -int main(int argc, char* argv[]) +void execute( + int DIM = 3, // dimension + int Q = 7, // number of discrete velocities + int model = SRT, // collision model + bool constvel = true, // velocity field is constant in time and space (for ADE) + bool bigprint = false, // use a more detailed decomposition of exported coefficients + bool verbosity = true, + bool EFDEprint = true, // export EFDE + bool EPDEprint = true, // export EPDE + bool factor_coefs = false, // use GiNaC::factor() when exporting coefficients to latex + int feqorder = 2, // -1 = symbolic, 1 = linear, 2 = quadratic + int ORDER = 2 // Taylor expansion order +) { - int DIM = 3; // dimension - int Q = 7; // number of discrete velocities - int model = SRT; // collision model - int ORDER = 2; // Taylor expansion order - - bool verbosity = true; - bool bigprint = true; // use a more detailed decomposition of exported coefficients - bool constvel = true; // velocity field is constant in time and space (for ADE) - bool EFDEprint = true; // export EFDE - bool EPDEprint = true; // export EPDE - bool factor_coefs = false; // use GiNaC::factor() when exporting coefficients to latex - int feqorder = -1; //-1 = symbolic - - printf("d=%d q=%d model=%d feqorder=%d constvel=%s bigprint=%d\n", DIM, Q, model, feqorder, (constvel)?"yes":"no", bigprint); fflush(stdout); @@ -89,6 +87,49 @@ int main(int argc, char* argv[]) if (verbosity) { printf("EPDE coefs computed\n"); fflush(stdout); } if (EPDEprint) for (int d=0;d<Q;d++) core.export_EPDE_coefs(d); +} + +void d1q3(bool constvel=true) +{ + execute(1,3,SRT,constvel); + execute(1,3,MRT1,constvel); + execute(1,3,CLBM1,constvel); +} + +void d2q5(bool constvel=true) +{ + bool bigprint=!constvel; + execute(2,5,SRT,constvel,bigprint); + execute(2,5,MRT1,constvel,bigprint); + execute(2,5,MRT2,constvel,bigprint); + execute(2,5,MRT1_OG,constvel,bigprint); + execute(2,5,MRT2_OG,constvel,bigprint); + execute(2,5,CLBM1,constvel,bigprint); + execute(2,5,CLBM2,constvel,bigprint); +} + +void d3q7(bool constvel=true) +{ + bool bigprint=!constvel; + execute(3,7,SRT,constvel,bigprint); + execute(3,7,MRT1,constvel,bigprint); + execute(3,7,MRT2,constvel,bigprint); + execute(3,7,MRT1_OG,constvel,bigprint); + execute(3,7,MRT2_OG,constvel,bigprint); + execute(3,7,CLBM1,constvel,bigprint); + execute(3,7,CLBM2,constvel,bigprint); +} + +int main(int argc, char* argv[]) +{ + d1q3(true); +// d1q3(false); + + d2q5(true); +// d2q5(false); + +// d3q7(true); +// d3q7(false); return 0; } diff --git a/taylor.cpp b/taylor.cpp index 50a7fda673aee513e93879d88cd6811cdd65b3d7..7cb951894d12085d5ad76086f4c28c7b4614ecbb 100644 --- a/taylor.cpp +++ b/taylor.cpp @@ -10,6 +10,10 @@ void TAYLOR::allocate(const char*comp, ex central_value) // allocate tay tay = new ex[(ORDER+1)*(ORDER+1)*(ORDER+1)*(ORDER+1)]; tay_tex = new ex[(ORDER+1)*(ORDER+1)*(ORDER+1)*(ORDER+1)]; +// tay_label = new ex[(ORDER+1)*(ORDER+1)*(ORDER+1)*(ORDER+1)]; + + pow_dl = new int[(ORDER+1)*(ORDER+1)*(ORDER+1)*(ORDER+1)]; + pow_dt = new int[(ORDER+1)*(ORDER+1)*(ORDER+1)*(ORDER+1)]; for (int k1=0;k1<=ORDER;k1++) for (int k2=0;k2<=ORDER;k2++) for (int k3=0;k3<=ORDER;k3++) @@ -17,42 +21,43 @@ void TAYLOR::allocate(const char*comp, ex central_value) { int k=k1+k2+k3+k4; int kx=k2+k3+k4; - sprintf(s5,""); - if (k1==1) sprintf(s5,"\\dt"); - if (k1>1) sprintf(s5,"\\dt^{%d}",k1); - sprintf(s6,""); - if (kx==1) sprintf(s6,"\\dl"); - if (kx>1) sprintf(s6,"\\dl^{%d}",kx); - +// sprintf(s5,""); +// if (k1==1) sprintf(s5,"\\dt"); +// if (k1>1) sprintf(s5,"\\dt^{%d}",k1); + pow_dt[indO(k1,k2,k3,k4)]=k1; +// sprintf(s6,""); +// if (kx==1) sprintf(s6,"\\dl"); +// if (kx>1) sprintf(s6,"\\dl^{%d}",kx); + pow_dl[indO(k1,k2,k3,k4)]=kx; + if (k1>0) { if (k1==1) sprintf(s1,"{\\partial t}"); else sprintf(s1,"{\\partial t^{%d}}",k1); } else sprintf(s1,""); if (k2>0) { if (k2==1) sprintf(s2,"{\\partial x}"); else sprintf(s2,"{\\partial x^{%d}}",k2); } else sprintf(s2,""); if (k3>0) { if (k3==1) sprintf(s3,"{\\partial y}"); else sprintf(s3,"{\\partial y^{%d}}",k3); } else sprintf(s3,""); if (k4>0) { if (k4==1) sprintf(s4,"{\\partial z}"); else sprintf(s4,"{\\partial z^{%d}}",k4); } else sprintf(s4,""); + + // tay if (k==0) sprintf(desc,"{%s}",comp); else if (k==1) - sprintf(desc,"%s%s\\frac{ \\partial {%s} }{%s%s%s%s}",s5,s6,comp,s1,s2,s3,s4); + sprintf(desc,"\\frac{ \\partial {%s} }{%s%s%s%s}",comp,s1,s2,s3,s4); else - sprintf(desc,"%s%s\\frac{ \\partial^{%d} {%s} }{%s%s%s%s}",s5,s6,k,comp,s1,s2,s3,s4); + sprintf(desc,"\\frac{ \\partial^{%d} {%s} }{%s%s%s%s}",k,comp,s1,s2,s3,s4); tay[indO(k1,k2,k3,k4)] = symbol(desc); + // tay tex sprintf(s1,""); for (int ik=0;ik<k1;ik++) sprintf(s1,"%st",s1); sprintf(s2,""); for (int ik=0;ik<k2;ik++) sprintf(s2,"%sx",s2); sprintf(s3,""); for (int ik=0;ik<k3;ik++) sprintf(s3,"%sy",s3); sprintf(s4,""); for (int ik=0;ik<k4;ik++) sprintf(s4,"%sz",s4); -// if (k1>0) { if (k1==1) sprintf(s1,"{t}"); else sprintf(s1,"{t^{%d}}",k1); } else sprintf(s1,""); -// if (k2>0) { if (k2==1) sprintf(s2,"{x}"); else sprintf(s2,"{x^{%d}}",k2); } else sprintf(s2,""); -// if (k3>0) { if (k3==1) sprintf(s3,"{y}"); else sprintf(s3,"{y^{%d}}",k3); } else sprintf(s3,""); -// if (k4>0) { if (k4==1) sprintf(s4,"{z}"); else sprintf(s4,"{z^{%d}}",k4); } else sprintf(s4,""); if (k==0) sprintf(desc,"{%s}",comp); else if (k==1) - sprintf(desc,"%s%s{\\partial_{%s%s%s%s}%s}",s5,s6,s1,s2,s3,s4,comp); + sprintf(desc,"{\\partial_{%s%s%s%s}%s}",s1,s2,s3,s4,comp); else - sprintf(desc,"%s%s{\\partial^{%d}_{%s%s%s%s}%s}",s5,s6,k,s1,s2,s3,s4,comp); + sprintf(desc,"{\\partial^{%d}_{%s%s%s%s}%s}",k,s1,s2,s3,s4,comp); tay_tex[indO(k1,k2,k3,k4)] = symbol(desc); } taylor_expand(); @@ -80,10 +85,11 @@ void TAYLOR::taylor_expand() if (j1+j2+j3==j) { ex koef=(ex)1; - if (k-j>0) koef*=pow((ex)l,k-j); - if (j1>0) koef*=pow((ex)x,j1); - if (j2>0) koef*=pow((ex)y,j2); - if (j3>0) koef*=pow((ex)z,j3); + if (k-j>0) koef*=pow((ex)l*dt,k-j); + if (j1>0) koef*=pow((ex)x*dl,j1); + if (j2>0) koef*=pow((ex)y*dl,j2); + if (j3>0) koef*=pow((ex)z*dl,j3); + sub[index(l,x,y,z)] += koef*tay[indO(k-j,j1,j2,j3)]/factorial(k-j)/factorial(j1)/factorial(j2)/factorial(j3); } } diff --git a/taylor.h b/taylor.h index 76fcad3e0af82d24d3027a95ba9fc35ffe0423b6..e331f4055147dbf4473715284d81ece14f9db965 100644 --- a/taylor.h +++ b/taylor.h @@ -38,6 +38,14 @@ struct TAYLOR : DEF ex *sub=0; ex central; + // this needs to be initialized + ex dl; + ex dt; + + // powers of \dl and \dt + int *pow_dl=0; + int *pow_dt=0; + void allocate(const char *comp, ex central_value); void taylor_expand(); @@ -46,8 +54,13 @@ struct TAYLOR : DEF ex& get_tay(int a, int b, int c, int d) { return tay[indO(a,b,c,d)]; } ex& get_tay_tex(int a, int b, int c, int d) { return tay_tex[indO(a,b,c,d)]; } - TAYLOR(int iDIM, int iQ, int _ORDER, int **external_index, int external_Nindex) : DEF(iDIM, iQ, external_index, external_Nindex) + int& get_pow_dl(int a, int b, int c, int d) { return pow_dl[indO(a,b,c,d)]; } + int& get_pow_dt(int a, int b, int c, int d) { return pow_dt[indO(a,b,c,d)]; } + + TAYLOR(int iDIM, int iQ, int _ORDER, int **external_index, int external_Nindex, ex sym_dl, ex sym_dt) : DEF(iDIM, iQ, external_index, external_Nindex) { + dl=sym_dl; + dt=sym_dt; ORDER=_ORDER; } @@ -56,6 +69,8 @@ struct TAYLOR : DEF if (tay) delete [] tay; if (tay_tex) delete [] tay_tex; if (sub) delete [] sub; + if (pow_dl) delete [] pow_dl; + if (pow_dt) delete [] pow_dt; } }; diff --git a/tex/buildall b/tex/buildall new file mode 100755 index 0000000000000000000000000000000000000000..f3446e1df62b29ef807d937692c627a0a0eb83c8 --- /dev/null +++ b/tex/buildall @@ -0,0 +1,14 @@ +#!/bin/bash +for a in supp*e.tex; do + buf_size=100000000 lualatex $a + buf_size=100000000 lualatex $a +done + +#clear aux files +rm -f *.aux +rm -f *.stl +rm -f *.log +rm -f *.out +rm -f *.toc + + diff --git a/tex/d1q3/d1q3_C.tex b/tex/d1q3/d1q3_C.tex new file mode 100644 index 0000000000000000000000000000000000000000..79fde2e695448988502fb720855898da2599ec6a --- /dev/null +++ b/tex/d1q3/d1q3_C.tex @@ -0,0 +1,10 @@ +Discrete velocity vectors: +\noindent +\begin{equation*} +\{ \vc_i \}_{i=1}^3 = +\left( + \colvec{1}{0}, + \colvec{1}{1}, + \colvec{1}{-1} +\right). +\end{equation*} diff --git a/tex/d1q3/d1q3_defs.tex b/tex/d1q3/d1q3_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..4c42f183e11a26c1952c3d3a4b7d8b4f2a03fbb6 --- /dev/null +++ b/tex/d1q3/d1q3_defs.tex @@ -0,0 +1,6 @@ +\newcommand{\mA}{m_{0}} +\newcommand{\kA}{k_{0}} +\newcommand{\mB}{m_{1}} +\newcommand{\kB}{k_{1}} +\newcommand{\mC}{m_{2}} +\newcommand{\kC}{k_{2}} diff --git a/tex/d1q3/d1q3_matM.tex b/tex/d1q3/d1q3_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..e4d2bf446f68ae4366bce6054114006d1779258e --- /dev/null +++ b/tex/d1q3/d1q3_matM.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{\hatM} = \begin{pmatrix} + 1 & 1 & 1\\ + 0 & 1 & -1\\ + 0 & 1 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3_matM_per_els.tex b/tex/d1q3/d1q3_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..0f872e462c06ceb065eb111f18f862441abd59ad --- /dev/null +++ b/tex/d1q3/d1q3_matM_per_els.tex @@ -0,0 +1,30 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{\hatM}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,3} = -1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,3} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m0_feq.tex b/tex/d1q3/d1q3m0_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..fc5925ecce7834ca6f0c13b26eac35ce63930f7e --- /dev/null +++ b/tex/d1q3/d1q3m0_feq.tex @@ -0,0 +1,9 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-c_s^{2}-u^{2}\\ + \frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + -\frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m0_matA.tex b/tex/d1q3/d1q3m0_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..681464acd1792d98185d1f4545eda0b8de45c74e --- /dev/null +++ b/tex/d1q3/d1q3m0_matA.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \omega & 0 & 0\\ + 0 & \omega & 0\\ + 0 & 0 & \omega\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m0_matA_per_els.tex b/tex/d1q3/d1q3m0_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..6da8d8ac7b92a5d081f263030b737f5f567b396e --- /dev/null +++ b/tex/d1q3/d1q3m0_matA_per_els.tex @@ -0,0 +1,31 @@ +Matrix $\matr{A}$: +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \omega. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m0_matB.tex b/tex/d1q3/d1q3m0_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..de9eca9d8a94242cf09f6578178942df1d82e16c --- /dev/null +++ b/tex/d1q3/d1q3m0_matB.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega & -1+\omega\\ + -1+\omega & 0 & -1+\omega\\ + -1+\omega & -1+\omega & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m0_matB_per_els.tex b/tex/d1q3/d1q3m0_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..220ccc2fb02045609f29f25622b7e2ae651b2cd9 --- /dev/null +++ b/tex/d1q3/d1q3m0_matB_per_els.tex @@ -0,0 +1,30 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m0_matM.tex b/tex/d1q3/d1q3m0_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..48bcd3f2e8be2c675bced8167a84043b96bf8f5a --- /dev/null +++ b/tex/d1q3/d1q3m0_matM.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 & 1 & 1\\ + 0 & 1 & -1\\ + 0 & 1 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m0_matM_per_els.tex b/tex/d1q3/d1q3m0_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..23ea857b7834d71203785c5561cc6175197d4538 --- /dev/null +++ b/tex/d1q3/d1q3m0_matM_per_els.tex @@ -0,0 +1,31 @@ +Matrix $\matr{M}$: +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m1_feq.tex b/tex/d1q3/d1q3m1_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..a68c07ed4e9e0df73e284d6390473c9ea5294717 --- /dev/null +++ b/tex/d1q3/d1q3m1_feq.tex @@ -0,0 +1,9 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-u^{2}-c_s^{2}\\ + \frac{1}{2} u^{2}+\frac{1}{2} u+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} u^{2}-\frac{1}{2} u+\frac{1}{2} c_s^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m1_matA.tex b/tex/d1q3/d1q3m1_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..435dde9b0a7b0697a980d8d7808674b0169cf019 --- /dev/null +++ b/tex/d1q3/d1q3m1_matA.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \omega_{0} & \omega_{0}-\omega_{2} & \omega_{0}-\omega_{2}\\ + 0 & \frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{1} & \frac{1}{2} \omega_{2}-\frac{1}{2} \omega_{1}\\ + 0 & \frac{1}{2} \omega_{2}-\frac{1}{2} \omega_{1} & \frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{1}\end{pmatrix}, +\end{equation*} diff --git a/tex/d1q3/d1q3m1_matA_per_els.tex b/tex/d1q3/d1q3m1_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..c9b0de06f4004059f82e8f7527d3f4ff0b78ab80 --- /dev/null +++ b/tex/d1q3/d1q3m1_matA_per_els.tex @@ -0,0 +1,30 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = \omega_{0}-\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = \omega_{0}-\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = \frac{1}{2} \omega_{2}-\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = \frac{1}{2} \omega_{2}-\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{1}, + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m1_matB.tex b/tex/d1q3/d1q3m1_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..f6ec9830f7289f52db578192f4c95d58fcfc0a0f --- /dev/null +++ b/tex/d1q3/d1q3m1_matB.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega_{2} & -1+\omega_{2}\\ + -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{1} & 0 & -1+\omega_{1}\\ + -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{1} & -1+\omega_{1} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m1_matB_per_els.tex b/tex/d1q3/d1q3m1_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..c2df1080f4dc57f7cca96a01c42e8586dc7dd4d0 --- /dev/null +++ b/tex/d1q3/d1q3m1_matB_per_els.tex @@ -0,0 +1,30 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m1_matM.tex b/tex/d1q3/d1q3m1_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..48bcd3f2e8be2c675bced8167a84043b96bf8f5a --- /dev/null +++ b/tex/d1q3/d1q3m1_matM.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 & 1 & 1\\ + 0 & 1 & -1\\ + 0 & 1 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m1_matM_per_els.tex b/tex/d1q3/d1q3m1_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..ed5fa733b3c28aecbc36c6dcf434f81858ce47c9 --- /dev/null +++ b/tex/d1q3/d1q3m1_matM_per_els.tex @@ -0,0 +1,30 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m5_feq.tex b/tex/d1q3/d1q3m5_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..340071cac31e8b314fdf08215b769d5393a22fc1 --- /dev/null +++ b/tex/d1q3/d1q3m5_feq.tex @@ -0,0 +1,9 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-u^{2}-c_s^{2}\\ + \frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}+\frac{1}{2} u\\ + \frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}-\frac{1}{2} u +\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m5_matA.tex b/tex/d1q3/d1q3m5_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..98c3cb8d00dc0b8fdc0a573d41cc2e2b7edc84cb --- /dev/null +++ b/tex/d1q3/d1q3m5_matA.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + 2 \omega_{1} u^{2}- u^{2} \omega_{2}+\omega_{0}- \omega_{0} u^{2} & {(2 \omega_{1} u-\omega_{0}- u {(\omega_{0}+\omega_{2})}+\omega_{2})} {(-1+u)} & {(2 \omega_{1} u+\omega_{0}- u {(\omega_{0}+\omega_{2})}-\omega_{2})} {(1+u)}\\ + -\frac{1}{2} {( \omega_{1} {(1+2 u)}-\omega_{0}- u {(\omega_{0}+\omega_{2})})} u & - \omega_{1} u^{2}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{1} u+\frac{1}{2} u^{2} \omega_{2}- u \omega_{2}+\frac{1}{2} \omega_{0} u^{2}+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{0} u & -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u {(\omega_{0}+\omega_{2})}-\omega_{2})} {(1+u)}\\ + -\frac{1}{2} {(\omega_{0}+ \omega_{1} {(-1+2 u)}- u {(\omega_{0}+\omega_{2})})} u & -\frac{1}{2} {(-1+u)} {( \omega_{1} {(-1+2 u)}- u {(\omega_{0}+\omega_{2})}+\omega_{2})} & - \omega_{1} u^{2}+\frac{1}{2} \omega_{1}-\frac{1}{2} \omega_{1} u+\frac{1}{2} u^{2} \omega_{2}+ u \omega_{2}+\frac{1}{2} \omega_{0} u^{2}+\frac{1}{2} \omega_{2}-\frac{1}{2} \omega_{0} u\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m5_matA_per_els.tex b/tex/d1q3/d1q3m5_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..fe00f94faec24c4ae5dcf483322f08747c1780c7 --- /dev/null +++ b/tex/d1q3/d1q3m5_matA_per_els.tex @@ -0,0 +1,30 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = 2 \omega_{1} u^{2}- u^{2} \omega_{2}+\omega_{0}- \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = {(2 \omega_{1} u-\omega_{0}- u {(\omega_{0}+\omega_{2})}+\omega_{2})} {(-1+u)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = {(2 \omega_{1} u+\omega_{0}- u {(\omega_{0}+\omega_{2})}-\omega_{2})} {(1+u)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = -\frac{1}{2} {( \omega_{1} {(1+2 u)}-\omega_{0}- u {(\omega_{0}+\omega_{2})})} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = - \omega_{1} u^{2}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{1} u+\frac{1}{2} u^{2} \omega_{2}- u \omega_{2}+\frac{1}{2} \omega_{0} u^{2}+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{0} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u {(\omega_{0}+\omega_{2})}-\omega_{2})} {(1+u)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = -\frac{1}{2} {(\omega_{0}+ \omega_{1} {(-1+2 u)}- u {(\omega_{0}+\omega_{2})})} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = -\frac{1}{2} {(-1+u)} {( \omega_{1} {(-1+2 u)}- u {(\omega_{0}+\omega_{2})}+\omega_{2})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = - \omega_{1} u^{2}+\frac{1}{2} \omega_{1}-\frac{1}{2} \omega_{1} u+\frac{1}{2} u^{2} \omega_{2}+ u \omega_{2}+\frac{1}{2} \omega_{0} u^{2}+\frac{1}{2} \omega_{2}-\frac{1}{2} \omega_{0} u. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m5_matB.tex b/tex/d1q3/d1q3m5_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..4fbb0393e2622b8e1f5c42f9b9c1daf22e55fcbd --- /dev/null +++ b/tex/d1q3/d1q3m5_matB.tex @@ -0,0 +1,7 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+2 \omega_{1} u-2 u \omega_{2}+\omega_{2} & -1-2 \omega_{1} u+2 u \omega_{2}+\omega_{2}\\ + -1+\frac{1}{2} \omega_{1}+ \omega_{1} u- u \omega_{2}+\frac{1}{2} \omega_{2} & 0 & -1+\omega_{1}+2 \omega_{1} u-2 u \omega_{2}\\ + -1+\frac{1}{2} \omega_{1}- \omega_{1} u+ u \omega_{2}+\frac{1}{2} \omega_{2} & -1+\omega_{1}-2 \omega_{1} u+2 u \omega_{2} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m5_matB_per_els.tex b/tex/d1q3/d1q3m5_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..0c583a4785828ef813272b63201534fd8ee31b18 --- /dev/null +++ b/tex/d1q3/d1q3m5_matB_per_els.tex @@ -0,0 +1,30 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+2 \omega_{1} u-2 u \omega_{2}+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1-2 \omega_{1} u+2 u \omega_{2}+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{2} \omega_{1}+ \omega_{1} u- u \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\omega_{1}+2 \omega_{1} u-2 u \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{2} \omega_{1}- \omega_{1} u+ u \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\omega_{1}-2 \omega_{1} u+2 u \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/d1q3m5_matK.tex b/tex/d1q3/d1q3m5_matK.tex new file mode 100644 index 0000000000000000000000000000000000000000..e6b3990f1d2c46d243db7d1c1db2d77f63b81ad4 --- /dev/null +++ b/tex/d1q3/d1q3m5_matK.tex @@ -0,0 +1,8 @@ +\noindent +\begin{equation*} +\matr{K} = \begin{pmatrix} + 1 &1 &1\\ + -u &1-u &-u-1\\ + u^2 &(1-u)^2 & (u+1)^2 +\end{pmatrix}. +\end{equation*} \ No newline at end of file diff --git a/tex/d1q3/d1q3m5_matK_per_els.tex b/tex/d1q3/d1q3m5_matK_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..e134a51486cee460c1cbd1e5b6255ff9d21e14f5 --- /dev/null +++ b/tex/d1q3/d1q3m5_matK_per_els.tex @@ -0,0 +1,30 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{K}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,1} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,2} = 1-u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,3} = (-u)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,1} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,2} = (1-u)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,3} = ((-u)-1)^2. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d1q3/d1q3m5_matM.tex b/tex/d1q3/d1q3m5_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..982016a71ba8b0a3c5fab5d43bf7cfb21e574edb --- /dev/null +++ b/tex/d1q3/d1q3m5_matM.tex @@ -0,0 +1,8 @@ +Matrix $\matr{M}$: +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 & 1 & 1\\ + 0 & 1 & -1\\ + 0 & 1 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d1q3/d1q3m5_matM_per_els.tex b/tex/d1q3/d1q3m5_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..23ea857b7834d71203785c5561cc6175197d4538 --- /dev/null +++ b/tex/d1q3/d1q3m5_matM_per_els.tex @@ -0,0 +1,31 @@ +Matrix $\matr{M}$: +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d1q3/supp_d1q3_defs.tex b/tex/d1q3/supp_d1q3_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..e8d97504d4229dad575d6ef0a2b413533feb3e7e --- /dev/null +++ b/tex/d1q3/supp_d1q3_defs.tex @@ -0,0 +1,15 @@ +\section{Global definitions} +In $\mathbb{R}$, the position and velocity vectors are given by $\vx=(x)$ and $\vu=(u)$, respectively. + +\noindent +\input{d1q3/d1q3_C} +\input{d1q3/d1q3m0_feq} +Lattice speed of sound: $c_s = \frac1{\sqrt{3}}$. + +\noindent +Moments $\vec{\mu} = \left( \mu_1, \mu_2, \mu_3 \right)^T$ are given by +$$ + \vec{\mu} = \matr{\hatM} \vec{f}, +$$ +where $\vec{f} = \left( f_1,f_2,f_3 \right)^T$ and +\input{d1q3/d1q3_matM} diff --git a/tex/d1q3/supp_d1q3m0_defs.tex b/tex/d1q3/supp_d1q3m0_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..68d047f6e00ae551a554aa0adcf8afaa63b8d56d --- /dev/null +++ b/tex/d1q3/supp_d1q3m0_defs.tex @@ -0,0 +1,11 @@ +\subsection{Definitions} +Matrix $\matr{A}=\matr{S}$: +\input{d1q3/d1q3m0_matA} +where +$$ + \matr{S} = \mathrm{diag}(\omega,\omega,\omega). +$$ + +\noindent +Matrix $\matr{B}$: +\input{d1q3/d1q3m0_matB} diff --git a/tex/d1q3/supp_d1q3m1_defs.tex b/tex/d1q3/supp_d1q3m1_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..fd5df17c5467720130ff2ab0864bceb06640db7e --- /dev/null +++ b/tex/d1q3/supp_d1q3m1_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d1q3/d1q3m1_matA} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2) +$$ +and +\input{d1q3/d1q3m1_matM} + +\noindent +Matrix $\matr{B}$: +\input{d1q3/d1q3m1_matB} diff --git a/tex/d1q3/supp_d1q3m5_defs.tex b/tex/d1q3/supp_d1q3m5_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..c616b065eef5c808dc79ff2e3053d0af16344626 --- /dev/null +++ b/tex/d1q3/supp_d1q3m5_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{K}^{-1} \matr{S} \matr{K}$: +\input{d1q3/d1q3m5_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2) +$$ +and +\input{d1q3/d1q3m5_matK} + +\noindent +Matrix $\matr{B}$: +\input{d1q3/d1q3m5_matB} diff --git a/tex/d2q5/d2q5_C.tex b/tex/d2q5/d2q5_C.tex new file mode 100644 index 0000000000000000000000000000000000000000..ef488bab7d8f8b1e3a42560a793e933507dc29cb --- /dev/null +++ b/tex/d2q5/d2q5_C.tex @@ -0,0 +1,12 @@ +Discrete velocity vectors: +\noindent +\begin{equation*} +\{ \vc_i \}_{i=1}^5 = +\left( + \colvec{2}{0}{0}, + \colvec{2}{1}{0}, + \colvec{2}{0}{1}, + \colvec{2}{-1}{0}, + \colvec{2}{0}{-1} +\right). +\end{equation*} diff --git a/tex/d2q5/d2q5_defs.tex b/tex/d2q5/d2q5_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..d17feb1946aa13a9222ca176cf8f62b8d051f082 --- /dev/null +++ b/tex/d2q5/d2q5_defs.tex @@ -0,0 +1,10 @@ +\newcommand{\mA}{m_{00}} +\newcommand{\kA}{k_{00}} +\newcommand{\mB}{m_{10}} +\newcommand{\kB}{k_{10}} +\newcommand{\mC}{m_{01}} +\newcommand{\kC}{k_{01}} +\newcommand{\mD}{m_{20}} +\newcommand{\kD}{k_{20}} +\newcommand{\mE}{m_{02}} +\newcommand{\kE}{k_{02}} diff --git a/tex/d2q5/d2q5_matM.tex b/tex/d2q5/d2q5_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..0fd35c025e272d8b1521f5260fda6bf4252bab8a --- /dev/null +++ b/tex/d2q5/d2q5_matM.tex @@ -0,0 +1,10 @@ +Matrix $\matr{M}$: +\noindent +\begin{equation*} +\matr{\hatM} = \begin{pmatrix} + 1 & 1 & 1 & 1 & 1\\ + 0 & 1 & 0 & -1 & 0\\ + 0 & 0 & 1 & 0 & -1\\ + 0 & 1 & 0 & 1 & 0\\ + 0 & 0 & 1 & 0 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5_matM_per_els.tex b/tex/d2q5/d2q5_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..e6f0789d52ac8f77128bf964c69e8a3a1760974e --- /dev/null +++ b/tex/d2q5/d2q5_matM_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{\hatM}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,4} = -1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,5} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m0_feq.tex b/tex/d2q5/d2q5m0_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..e9f634da25cb5ea4732bb61bbd5db1cd3ab76ed5 --- /dev/null +++ b/tex/d2q5/d2q5m0_feq.tex @@ -0,0 +1,11 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-u^{2}-2 c_s^{2}-v^{2}\\ + \frac{1}{2} u+\frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} v+\frac{1}{2} c_s^{2}+\frac{1}{2} v^{2}\\ + -\frac{1}{2} u+\frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}\\ + -\frac{1}{2} v+\frac{1}{2} c_s^{2}+\frac{1}{2} v^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m0_matA.tex b/tex/d2q5/d2q5m0_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..6bb4990756a6ace0f620a1698ef23aa902891095 --- /dev/null +++ b/tex/d2q5/d2q5m0_matA.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \omega & 0 & 0 & 0 & 0\\ + 0 & \omega & 0 & 0 & 0\\ + 0 & 0 & \omega & 0 & 0\\ + 0 & 0 & 0 & \omega & 0\\ + 0 & 0 & 0 & 0 & \omega\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m0_matA_per_els.tex b/tex/d2q5/d2q5m0_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..e63bd695d916548ccb8c009708a6c57fffe8081c --- /dev/null +++ b/tex/d2q5/d2q5m0_matA_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \omega. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m0_matB.tex b/tex/d2q5/d2q5m0_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..d71c49d8a27aeb77e184412d9408d1106d00de42 --- /dev/null +++ b/tex/d2q5/d2q5m0_matB.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega & -1+\omega & -1+\omega & -1+\omega\\ + -1+\omega & 0 & -1+\omega & -1+\omega & -1+\omega\\ + -1+\omega & -1+\omega & 0 & -1+\omega & -1+\omega\\ + -1+\omega & -1+\omega & -1+\omega & 0 & -1+\omega\\ + -1+\omega & -1+\omega & -1+\omega & -1+\omega & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m0_matB_per_els.tex b/tex/d2q5/d2q5m0_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..80e674897aefcb108afa4b47172df5d4d04a33da --- /dev/null +++ b/tex/d2q5/d2q5m0_matB_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\omega, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m0_matM.tex b/tex/d2q5/d2q5m0_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..43aa7a82336fddfc955dc422424c75de5378125a --- /dev/null +++ b/tex/d2q5/d2q5m0_matM.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 & 1 & 1 & 1 & 1\\ + 0 & 1 & 0 & -1 & 0\\ + 0 & 0 & 1 & 0 & -1\\ + 0 & 1 & 0 & 1 & 0\\ + 0 & 0 & 1 & 0 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m0_matM_per_els.tex b/tex/d2q5/d2q5m0_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..3fe471248372b05d1988f81a7028264c5d2e871a --- /dev/null +++ b/tex/d2q5/d2q5m0_matM_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m1_feq.tex b/tex/d2q5/d2q5m1_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..e034b98df186b56cd454e50ee70d644049161738 --- /dev/null +++ b/tex/d2q5/d2q5m1_feq.tex @@ -0,0 +1,11 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-2 c_s^{2}-v^{2}-u^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}+\frac{1}{2} u\\ + \frac{1}{2} v+\frac{1}{2} c_s^{2}+\frac{1}{2} v^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}-\frac{1}{2} u\\ + -\frac{1}{2} v+\frac{1}{2} c_s^{2}+\frac{1}{2} v^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m1_matA.tex b/tex/d2q5/d2q5m1_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..8d4daf412049c12082c717155017716142ef6e23 --- /dev/null +++ b/tex/d2q5/d2q5m1_matA.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \omega_{0} & -\omega_{3}+\omega_{0} & \omega_{0}-\omega_{4} & -\omega_{3}+\omega_{0} & \omega_{0}-\omega_{4}\\ + 0 & \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & 0 & -\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & 0\\ + 0 & 0 & \frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4} & 0 & -\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}\\ + 0 & -\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & 0 & \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & 0\\ + 0 & 0 & -\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4} & 0 & \frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m1_matA_per_els.tex b/tex/d2q5/d2q5m1_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..c82227673ab69fc4a4a23922891fc43fcf3ded92 --- /dev/null +++ b/tex/d2q5/d2q5m1_matA_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -\omega_{3}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = \omega_{0}-\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = -\omega_{3}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = \omega_{0}-\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = -\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = -\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = -\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = -\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m1_matB.tex b/tex/d2q5/d2q5m1_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..acf9647f3abd125da0ba00c4f86380a5f0486c8a --- /dev/null +++ b/tex/d2q5/d2q5m1_matB.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega_{3} & -1+\omega_{4} & -1+\omega_{3} & -1+\omega_{4}\\ + -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & 0 & -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}\\ + -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4} & -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4} & 0 & -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4} & -1+\omega_{2}\\ + -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & 0 & -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}\\ + -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4} & -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4} & -1+\omega_{2} & -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m1_matB_per_els.tex b/tex/d2q5/d2q5m1_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..2eeac38615d0698d6c1d7f8cf80d796c7e028ab1 --- /dev/null +++ b/tex/d2q5/d2q5m1_matB_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m1_matM.tex b/tex/d2q5/d2q5m1_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..43aa7a82336fddfc955dc422424c75de5378125a --- /dev/null +++ b/tex/d2q5/d2q5m1_matM.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 & 1 & 1 & 1 & 1\\ + 0 & 1 & 0 & -1 & 0\\ + 0 & 0 & 1 & 0 & -1\\ + 0 & 1 & 0 & 1 & 0\\ + 0 & 0 & 1 & 0 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m1_matM_per_els.tex b/tex/d2q5/d2q5m1_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..3fe471248372b05d1988f81a7028264c5d2e871a --- /dev/null +++ b/tex/d2q5/d2q5m1_matM_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m2_feq.tex b/tex/d2q5/d2q5m2_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..84489f9127394d69ef5e54d761ff60dc5df46fb0 --- /dev/null +++ b/tex/d2q5/d2q5m2_feq.tex @@ -0,0 +1,11 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-v^{2}-2 c_s^{2}-u^{2}\\ + \frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + \frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}+\frac{1}{2} v\\ + -\frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + \frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}-\frac{1}{2} v +\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m2_matA.tex b/tex/d2q5/d2q5m2_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..b6b4ae7989136fd2acbbf626ba2ac5c55bb4ec19 --- /dev/null +++ b/tex/d2q5/d2q5m2_matA.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \omega_{0} & -\omega_{3}+\omega_{0} & -\omega_{3}+\omega_{0} & -\omega_{3}+\omega_{0} & -\omega_{3}+\omega_{0}\\ + 0 & \frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3} & -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3} & \frac{1}{4} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3} & -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}\\ + 0 & -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3} & \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2} & -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3} & \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}-\frac{1}{2} \omega_{2}\\ + 0 & \frac{1}{4} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3} & -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3} & \frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3} & -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}\\ + 0 & -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3} & \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}-\frac{1}{2} \omega_{2} & \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3} & \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m2_matA_per_els.tex b/tex/d2q5/d2q5m2_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..eca9a11d375684a6238f11fbc4c189e5ee47ca00 --- /dev/null +++ b/tex/d2q5/d2q5m2_matA_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -\omega_{3}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -\omega_{3}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = -\omega_{3}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = -\omega_{3}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = \frac{1}{4} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = \frac{1}{4} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = -\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m2_matB.tex b/tex/d2q5/d2q5m2_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..4c33bdb764ded930f24aaa228a5c623938b5c020 --- /dev/null +++ b/tex/d2q5/d2q5m2_matB.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega_{3} & -1+\omega_{3} & -1+\omega_{3} & -1+\omega_{3}\\ + -1+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & -1+\omega_{2}\\ + -1+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{2} \omega_{2} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m2_matB_per_els.tex b/tex/d2q5/d2q5m2_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..2223d64fd480592ddc1dc9c834864666ca47c4f4 --- /dev/null +++ b/tex/d2q5/d2q5m2_matB_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m2_matM.tex b/tex/d2q5/d2q5m2_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..072bf449ba3fa2731d630e627265e9cfebda3efe --- /dev/null +++ b/tex/d2q5/d2q5m2_matM.tex @@ -0,0 +1,10 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 &1 &1 &1 &1\\ + 0 &1 &0 &-1 &0\\ + 0 &0 &1 &0 &-1\\ + 0 &1 &1 &1 &1\\ + 0 &1 &-1 &1 &-1 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m2_matM_per_els.tex b/tex/d2q5/d2q5m2_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..415a88a393147b2f5fc5185157e9677f7fb6c13d --- /dev/null +++ b/tex/d2q5/d2q5m2_matM_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = -1. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m3_feq.tex b/tex/d2q5/d2q5m3_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..1eddee0e7bf5aec2324e4e4f13a04b9a51d79dfd --- /dev/null +++ b/tex/d2q5/d2q5m3_feq.tex @@ -0,0 +1,11 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-u^{2}-v^{2}-2 c_s^{2}\\ + \frac{1}{2} u^{2}+\frac{1}{2} u+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} v^{2}+\frac{1}{2} v+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} u^{2}-\frac{1}{2} u+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} v^{2}-\frac{1}{2} v+\frac{1}{2} c_s^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m3_matA.tex b/tex/d2q5/d2q5m3_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..5d8b5a16c4eecf4fc73b3eb68e6c6d4d2f39772a --- /dev/null +++ b/tex/d2q5/d2q5m3_matA.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \frac{2}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}\\ + -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{2} \omega_{1}+\frac{3}{10} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{2} \omega_{1}+\frac{3}{10} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}\\ + -\frac{1}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{6} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}+\frac{1}{2} \omega_{2} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{6} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}-\frac{1}{2} \omega_{2}\\ + -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{2} \omega_{1}+\frac{3}{10} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{2} \omega_{1}+\frac{3}{10} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}\\ + -\frac{1}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{6} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}-\frac{1}{2} \omega_{2} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{6} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}+\frac{1}{2} \omega_{2}\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m3_matA_per_els.tex b/tex/d2q5/d2q5m3_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..80875f31e2e38d384b47f6bbdfe7b9bbf549a884 --- /dev/null +++ b/tex/d2q5/d2q5m3_matA_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \frac{2}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -\frac{1}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = -\frac{1}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{2} \omega_{1}+\frac{3}{10} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = -\frac{1}{2} \omega_{1}+\frac{3}{10} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = -\frac{1}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{6} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = \frac{1}{6} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = -\frac{1}{2} \omega_{1}+\frac{3}{10} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{2} \omega_{1}+\frac{3}{10} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = -\frac{1}{3} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = \frac{1}{6} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{6} \omega_{4}+\frac{2}{15} \omega_{3}+\frac{1}{5} \omega_{0}+\frac{1}{2} \omega_{2}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m3_matB.tex b/tex/d2q5/d2q5m3_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..cb8a27472047d504937103b4f141849444288d81 --- /dev/null +++ b/tex/d2q5/d2q5m3_matB.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\frac{2}{3} \omega_{4}+\frac{1}{3} \omega_{3} & -1+\omega_{4} & -1+\frac{2}{3} \omega_{4}+\frac{1}{3} \omega_{3} & -1+\omega_{4}\\ + -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & 0 & -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}\\ + -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{3}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{3}+\frac{1}{2} \omega_{2} & -1+\omega_{2}\\ + -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3} & 0 & -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}\\ + -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{3}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{3}+\frac{1}{2} \omega_{2} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m3_matB_per_els.tex b/tex/d2q5/d2q5m3_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..4b164a020f2d033a67898a1efb039dac38f3a182 --- /dev/null +++ b/tex/d2q5/d2q5m3_matB_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\frac{2}{3} \omega_{4}+\frac{1}{3} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\frac{2}{3} \omega_{4}+\frac{1}{3} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m3_matM.tex b/tex/d2q5/d2q5m3_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..de60625e5c2dfe2d0c79d4166f26c24823a8e378 --- /dev/null +++ b/tex/d2q5/d2q5m3_matM.tex @@ -0,0 +1,10 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 &1 &1 &1 &1\\ + 0 &1 &0 &-1 &0\\ + 0 &0 &1 &0 &-1\\ + -2 &3 &-2 &3 &-2\\ + -2 &0 &1 &0 &1 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m3_matM_per_els.tex b/tex/d2q5/d2q5m3_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..75637529ca6e28d0c3a027a66d5cfcc3b8e5d895 --- /dev/null +++ b/tex/d2q5/d2q5m3_matM_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 3, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 3, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m4_feq.tex b/tex/d2q5/d2q5m4_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..00e806eb318ca17cc770347974980183160f3028 --- /dev/null +++ b/tex/d2q5/d2q5m4_feq.tex @@ -0,0 +1,11 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-2 c_s^{2}-v^{2}-u^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} u+\frac{1}{2} u^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} v^{2}+\frac{1}{2} v\\ + \frac{1}{2} c_s^{2}-\frac{1}{2} u+\frac{1}{2} u^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} v^{2}-\frac{1}{2} v +\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m4_matA.tex b/tex/d2q5/d2q5m4_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..bb2f4ded27da13b105b0c86ef436bdf3b17514de --- /dev/null +++ b/tex/d2q5/d2q5m4_matA.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \frac{4}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}\\ + -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{4} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}\\ + -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}+\frac{1}{2} \omega_{2} & -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}-\frac{1}{2} \omega_{2}\\ + -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{4} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}\\ + -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0} & -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}-\frac{1}{2} \omega_{2} & -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0} & \frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}+\frac{1}{2} \omega_{2}\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m4_matA_per_els.tex b/tex/d2q5/d2q5m4_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..b6b5bf802486aefc5a4d43bad6ef27a9d4a53c7c --- /dev/null +++ b/tex/d2q5/d2q5m4_matA_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \frac{4}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = \frac{1}{4} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = \frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = \frac{1}{4} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = -\frac{1}{5} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = \frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = -\frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{4} \omega_{4}+\frac{1}{20} \omega_{3}+\frac{1}{5} \omega_{0}+\frac{1}{2} \omega_{2}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m4_matB.tex b/tex/d2q5/d2q5m4_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..5113bafa95440c753a7cc2c8f3ff4828f9f33ace --- /dev/null +++ b/tex/d2q5/d2q5m4_matB.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega_{3} & -1+\omega_{3} & -1+\omega_{3} & -1+\omega_{3}\\ + -1+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & -1+\omega_{2}\\ + -1+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m4_matB_per_els.tex b/tex/d2q5/d2q5m4_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..b89adcdaad7151db8605b1452849afec58901b24 --- /dev/null +++ b/tex/d2q5/d2q5m4_matB_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{4} \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m4_matM.tex b/tex/d2q5/d2q5m4_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..30da2cc661f7c7ff73200afd4b3094c650132271 --- /dev/null +++ b/tex/d2q5/d2q5m4_matM.tex @@ -0,0 +1,10 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 &1 &1 &1 &1\\ + 0 &1 &0 &-1 &0\\ + 0 &0 &1 &0 &-1\\ + -2^2 &1 &1 &1 &1\\ + 0 &1 &-1 &1 &-1 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m4_matM_per_els.tex b/tex/d2q5/d2q5m4_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..b0ba6c534ea74c64bc7eae89389faf9d7119bbed --- /dev/null +++ b/tex/d2q5/d2q5m4_matM_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = -2^2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = -1. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m5_feq.tex b/tex/d2q5/d2q5m5_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..d4b980b5a13b980b3b98d8cd8888cce844ef1620 --- /dev/null +++ b/tex/d2q5/d2q5m5_feq.tex @@ -0,0 +1,11 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-u^{2}-v^{2}-2 c_s^{2}\\ + \frac{1}{2} u+\frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} v+\frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}\\ + -\frac{1}{2} u+\frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}\\ + -\frac{1}{2} v+\frac{1}{2} v^{2}+\frac{1}{2} c_s^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m5_matA.tex b/tex/d2q5/d2q5m5_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..85856780ec2e691382bc05c2b96e81ba07725a3f --- /dev/null +++ b/tex/d2q5/d2q5m5_matA.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + - \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}- v^{2} \omega_{0}+2 u^{2} \omega_{1} & -2 u \omega_{1}-\omega_{3}- \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}+2 u \omega_{3}- v^{2} \omega_{0}+2 u^{2} \omega_{1} & 2 \omega_{4} v-\omega_{4}- \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}-2 v \omega_{2}- v^{2} \omega_{0}+2 u^{2} \omega_{1} & 2 u \omega_{1}-\omega_{3}- \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}-2 u \omega_{3}- v^{2} \omega_{0}+2 u^{2} \omega_{1} & -2 \omega_{4} v-\omega_{4}- \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}+2 v \omega_{2}- v^{2} \omega_{0}+2 u^{2} \omega_{1}\\ + \frac{1}{2} u {(\omega_{0}- \omega_{1} {(1+2 u)}+ u {(\omega_{3}+\omega_{0})})} & \frac{1}{2} u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} u \omega_{0}+\frac{1}{2} \omega_{3}+\frac{1}{2} u^{2} \omega_{3}+\frac{1}{2} u^{2} \omega_{0}- u \omega_{3}- u^{2} \omega_{1} & \frac{1}{2} u {(\omega_{0}- \omega_{1} {(1+2 u)}+ u {(\omega_{3}+\omega_{0})})} & \frac{1}{2} {(\omega_{3}- \omega_{1} {(1+2 u)}+ u {(\omega_{3}+\omega_{0})})} {(1+u)} & \frac{1}{2} u {(\omega_{0}- \omega_{1} {(1+2 u)}+ u {(\omega_{3}+\omega_{0})})}\\ + \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v+\omega_{0}-\omega_{2})} & \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v+\omega_{0}-\omega_{2})} & - \omega_{4} v+\frac{1}{2} \omega_{4}+\frac{1}{2} v \omega_{0}+\frac{1}{2} \omega_{4} v^{2}- v^{2} \omega_{2}+\frac{1}{2} v \omega_{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{2} \omega_{2} & \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v+\omega_{0}-\omega_{2})} & \frac{1}{2} {(1+v)} {( {(\omega_{0}-2 \omega_{2})} v-\omega_{2}+ {(1+v)} \omega_{4})}\\ + -\frac{1}{2} u {(\omega_{0}- u {(\omega_{3}+\omega_{0})}+ {(-1+2 u)} \omega_{1})} & -\frac{1}{2} {(\omega_{3}- u {(\omega_{3}+\omega_{0})}+ {(-1+2 u)} \omega_{1})} {(-1+u)} & -\frac{1}{2} u {(\omega_{0}- u {(\omega_{3}+\omega_{0})}+ {(-1+2 u)} \omega_{1})} & -\frac{1}{2} u \omega_{1}+\frac{1}{2} \omega_{1}-\frac{1}{2} u \omega_{0}+\frac{1}{2} \omega_{3}+\frac{1}{2} u^{2} \omega_{3}+\frac{1}{2} u^{2} \omega_{0}+ u \omega_{3}- u^{2} \omega_{1} & -\frac{1}{2} u {(\omega_{0}- u {(\omega_{3}+\omega_{0})}+ {(-1+2 u)} \omega_{1})}\\ + \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v-\omega_{0}+\omega_{2})} & \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v-\omega_{0}+\omega_{2})} & \frac{1}{2} {( {(\omega_{0}-2 \omega_{2})} v+ \omega_{4} {(-1+v)}+\omega_{2})} {(-1+v)} & \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v-\omega_{0}+\omega_{2})} & \omega_{4} v+\frac{1}{2} \omega_{4}-\frac{1}{2} v \omega_{0}+\frac{1}{2} \omega_{4} v^{2}- v^{2} \omega_{2}-\frac{1}{2} v \omega_{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{2} \omega_{2}\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m5_matA_per_els.tex b/tex/d2q5/d2q5m5_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..f786005e6ea3afa659fc324bbb8867e9b8b12e29 --- /dev/null +++ b/tex/d2q5/d2q5m5_matA_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = - \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}- v^{2} \omega_{0}+2 u^{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -2 u \omega_{1}-\omega_{3}- \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}+2 u \omega_{3}- v^{2} \omega_{0}+2 u^{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = 2 \omega_{4} v-\omega_{4}- \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}-2 v \omega_{2}- v^{2} \omega_{0}+2 u^{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = 2 u \omega_{1}-\omega_{3}- \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}-2 u \omega_{3}- v^{2} \omega_{0}+2 u^{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = -2 \omega_{4} v-\omega_{4}- \omega_{4} v^{2}+2 v^{2} \omega_{2}- u^{2} \omega_{3}- u^{2} \omega_{0}+\omega_{0}+2 v \omega_{2}- v^{2} \omega_{0}+2 u^{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = \frac{1}{2} u {(\omega_{0}- \omega_{1} {(1+2 u)}+ u {(\omega_{3}+\omega_{0})})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{2} u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} u \omega_{0}+\frac{1}{2} \omega_{3}+\frac{1}{2} u^{2} \omega_{3}+\frac{1}{2} u^{2} \omega_{0}- u \omega_{3}- u^{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = \frac{1}{2} u {(\omega_{0}- \omega_{1} {(1+2 u)}+ u {(\omega_{3}+\omega_{0})})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = \frac{1}{2} {(\omega_{3}- \omega_{1} {(1+2 u)}+ u {(\omega_{3}+\omega_{0})})} {(1+u)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = \frac{1}{2} u {(\omega_{0}- \omega_{1} {(1+2 u)}+ u {(\omega_{3}+\omega_{0})})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v+\omega_{0}-\omega_{2})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v+\omega_{0}-\omega_{2})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = - \omega_{4} v+\frac{1}{2} \omega_{4}+\frac{1}{2} v \omega_{0}+\frac{1}{2} \omega_{4} v^{2}- v^{2} \omega_{2}+\frac{1}{2} v \omega_{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v+\omega_{0}-\omega_{2})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = \frac{1}{2} {(1+v)} {( {(\omega_{0}-2 \omega_{2})} v-\omega_{2}+ {(1+v)} \omega_{4})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = -\frac{1}{2} u {(\omega_{0}- u {(\omega_{3}+\omega_{0})}+ {(-1+2 u)} \omega_{1})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = -\frac{1}{2} {(\omega_{3}- u {(\omega_{3}+\omega_{0})}+ {(-1+2 u)} \omega_{1})} {(-1+u)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = -\frac{1}{2} u {(\omega_{0}- u {(\omega_{3}+\omega_{0})}+ {(-1+2 u)} \omega_{1})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = -\frac{1}{2} u \omega_{1}+\frac{1}{2} \omega_{1}-\frac{1}{2} u \omega_{0}+\frac{1}{2} \omega_{3}+\frac{1}{2} u^{2} \omega_{3}+\frac{1}{2} u^{2} \omega_{0}+ u \omega_{3}- u^{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = -\frac{1}{2} u {(\omega_{0}- u {(\omega_{3}+\omega_{0})}+ {(-1+2 u)} \omega_{1})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v-\omega_{0}+\omega_{2})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v-\omega_{0}+\omega_{2})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = \frac{1}{2} {( {(\omega_{0}-2 \omega_{2})} v+ \omega_{4} {(-1+v)}+\omega_{2})} {(-1+v)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = \frac{1}{2} v {( \omega_{4} v+ {(\omega_{0}-2 \omega_{2})} v-\omega_{0}+\omega_{2})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \omega_{4} v+\frac{1}{2} \omega_{4}-\frac{1}{2} v \omega_{0}+\frac{1}{2} \omega_{4} v^{2}- v^{2} \omega_{2}-\frac{1}{2} v \omega_{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{2} \omega_{2}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m5_matB.tex b/tex/d2q5/d2q5m5_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..0f16bf1134353c1672c7bc8bfa3273a3a10ab2df --- /dev/null +++ b/tex/d2q5/d2q5m5_matB.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+2 u \omega_{1}+\omega_{3}-2 u \omega_{3} & -1-2 \omega_{4} v+\omega_{4}+2 v \omega_{2} & -1-2 u \omega_{1}+\omega_{3}+2 u \omega_{3} & -1+2 \omega_{4} v+\omega_{4}-2 v \omega_{2}\\ + -1+ u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}- u \omega_{3} & 0 & -1+ u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}- u \omega_{3} & -1+2 u \omega_{1}+\omega_{1}-2 u \omega_{3} & -1+ u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}- u \omega_{3}\\ + -1- \omega_{4} v+\frac{1}{2} \omega_{4}+ v \omega_{2}+\frac{1}{2} \omega_{2} & -1- \omega_{4} v+\frac{1}{2} \omega_{4}+ v \omega_{2}+\frac{1}{2} \omega_{2} & 0 & -1- \omega_{4} v+\frac{1}{2} \omega_{4}+ v \omega_{2}+\frac{1}{2} \omega_{2} & -1-2 \omega_{4} v+2 v \omega_{2}+\omega_{2}\\ + -1- u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}+ u \omega_{3} & -1-2 u \omega_{1}+\omega_{1}+2 u \omega_{3} & -1- u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}+ u \omega_{3} & 0 & -1- u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}+ u \omega_{3}\\ + -1+ \omega_{4} v+\frac{1}{2} \omega_{4}- v \omega_{2}+\frac{1}{2} \omega_{2} & -1+ \omega_{4} v+\frac{1}{2} \omega_{4}- v \omega_{2}+\frac{1}{2} \omega_{2} & -1+2 \omega_{4} v-2 v \omega_{2}+\omega_{2} & -1+ \omega_{4} v+\frac{1}{2} \omega_{4}- v \omega_{2}+\frac{1}{2} \omega_{2} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m5_matB_per_els.tex b/tex/d2q5/d2q5m5_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..5b7c5c7b33ac218f1ba9ccec3667c7aeac11e819 --- /dev/null +++ b/tex/d2q5/d2q5m5_matB_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+2 u \omega_{1}+\omega_{3}-2 u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1-2 \omega_{4} v+\omega_{4}+2 v \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1-2 u \omega_{1}+\omega_{3}+2 u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+2 \omega_{4} v+\omega_{4}-2 v \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+ u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}- u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+ u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}- u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+2 u \omega_{1}+\omega_{1}-2 u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+ u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}- u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1- \omega_{4} v+\frac{1}{2} \omega_{4}+ v \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1- \omega_{4} v+\frac{1}{2} \omega_{4}+ v \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1- \omega_{4} v+\frac{1}{2} \omega_{4}+ v \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1-2 \omega_{4} v+2 v \omega_{2}+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1- u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}+ u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1-2 u \omega_{1}+\omega_{1}+2 u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1- u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}+ u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1- u \omega_{1}+\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{3}+ u \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+ \omega_{4} v+\frac{1}{2} \omega_{4}- v \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+ \omega_{4} v+\frac{1}{2} \omega_{4}- v \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+2 \omega_{4} v-2 v \omega_{2}+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+ \omega_{4} v+\frac{1}{2} \omega_{4}- v \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m5_matK.tex b/tex/d2q5/d2q5m5_matK.tex new file mode 100644 index 0000000000000000000000000000000000000000..801bb80fd844587593b212314cdf0d8be1672e90 --- /dev/null +++ b/tex/d2q5/d2q5m5_matK.tex @@ -0,0 +1,10 @@ +\noindent +\begin{equation*} +\matr{K} = \begin{pmatrix} + 1 &1 &1 &1 &1\\ + -u &1-u &-u &-u-1 &-u\\ + -v &-v &1-v &-v &-v-1\\ + u^2 &(1-u)^2 &u^2 &(u+1)^2 &u^2\\ + v^2 &v^2 &(1-v)^2 &v^2 &(v+1)^2 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m5_matK_per_els.tex b/tex/d2q5/d2q5m5_matK_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..c51471cc07f4af214f6cfd0e71fcae0e4fc19d3f --- /dev/null +++ b/tex/d2q5/d2q5m5_matK_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{K}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,1} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,2} = 1-u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,3} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,4} = (-u)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,5} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,1} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,2} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,3} = 1-v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,4} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,5} = (-v)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,1} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,2} = (1-u)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,3} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,4} = ((-u)-1)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,5} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,1} = v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,2} = v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,3} = (1-v)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,4} = v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,5} = ((-v)-1)^2. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m6_feq.tex b/tex/d2q5/d2q5m6_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..a0d69d0606243693f7a97b560055183e995387e4 --- /dev/null +++ b/tex/d2q5/d2q5m6_feq.tex @@ -0,0 +1,11 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-v^{2}-2 c_s^{2}-u^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} u+\frac{1}{2} u^{2}\\ + \frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}+\frac{1}{2} v\\ + \frac{1}{2} c_s^{2}-\frac{1}{2} u+\frac{1}{2} u^{2}\\ + \frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}-\frac{1}{2} v +\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m6_matA.tex b/tex/d2q5/d2q5m6_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..27c0bf37a26b89b1ade68c6b1b39966d78241111 --- /dev/null +++ b/tex/d2q5/d2q5m6_matA.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}- \omega_{3} v^{2}- \omega_{0} u^{2}- v^{2} \omega_{0} & 2 \omega_{3} u-\omega_{3}+\omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}-2 u \omega_{1}- \omega_{3} v^{2}- \omega_{0} u^{2}- v^{2} \omega_{0} & -\omega_{3}+\omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}-2 v \omega_{2}- \omega_{3} v^{2}+2 \omega_{3} v- \omega_{0} u^{2}- v^{2} \omega_{0} & -2 \omega_{3} u-\omega_{3}+\omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}+2 u \omega_{1}- \omega_{3} v^{2}- \omega_{0} u^{2}- v^{2} \omega_{0} & -\omega_{3}+\omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}+2 v \omega_{2}- \omega_{3} v^{2}-2 \omega_{3} v- \omega_{0} u^{2}- v^{2} \omega_{0}\\ + \frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2} & -\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{1}{2} u \omega_{1}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} \omega_{1} & \frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u-\frac{1}{2} \omega_{3} v-\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2} & \frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{3}{2} u \omega_{1}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}-\frac{1}{2} \omega_{1} & -\frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{2} \omega_{3} v-\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}\\ + \frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0} & \frac{1}{2} v \omega_{0}-\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} v \omega_{2}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0} & -\frac{1}{2} v \omega_{4}+\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} \omega_{2}+\frac{1}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0} & \frac{1}{2} v \omega_{0}+\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} v \omega_{2}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0} & \frac{1}{2} v \omega_{4}+\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} \omega_{2}-\frac{3}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}\\ + \frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2} & -\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{3}{2} u \omega_{1}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}-\frac{1}{2} \omega_{1} & \frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u-\frac{1}{2} \omega_{3} v-\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2} & \frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{1}{2} u \omega_{1}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} \omega_{1} & -\frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{2} \omega_{3} v-\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}\\ + -\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0} & -\frac{1}{2} v \omega_{0}-\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} v \omega_{2}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0} & -\frac{1}{2} v \omega_{4}-\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} \omega_{2}+\frac{3}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0} & -\frac{1}{2} v \omega_{0}+\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} v \omega_{2}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0} & \frac{1}{2} v \omega_{4}-\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} \omega_{2}-\frac{1}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m6_matA_per_els.tex b/tex/d2q5/d2q5m6_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..eca1a249998e762214eea8b7bc774deead46f9e5 --- /dev/null +++ b/tex/d2q5/d2q5m6_matA_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}- \omega_{3} v^{2}- \omega_{0} u^{2}- v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = 2 \omega_{3} u-\omega_{3}+\omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}-2 u \omega_{1}- \omega_{3} v^{2}- \omega_{0} u^{2}- v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -\omega_{3}+\omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}-2 v \omega_{2}- \omega_{3} v^{2}+2 \omega_{3} v- \omega_{0} u^{2}- v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = -2 \omega_{3} u-\omega_{3}+\omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}+2 u \omega_{1}- \omega_{3} v^{2}- \omega_{0} u^{2}- v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = -\omega_{3}+\omega_{0}- \omega_{3} u^{2}+2 u^{2} \omega_{1}+2 v^{2} \omega_{2}+2 v \omega_{2}- \omega_{3} v^{2}-2 \omega_{3} v- \omega_{0} u^{2}- v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = \frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = -\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{1}{2} u \omega_{1}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = \frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u-\frac{1}{2} \omega_{3} v-\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = \frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{3}{2} u \omega_{1}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}-\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = -\frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{2} \omega_{3} v-\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = \frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = \frac{1}{2} v \omega_{0}-\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} v \omega_{2}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = -\frac{1}{2} v \omega_{4}+\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} \omega_{2}+\frac{1}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = \frac{1}{2} v \omega_{0}+\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} v \omega_{2}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = \frac{1}{2} v \omega_{4}+\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} \omega_{2}-\frac{3}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = \frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = -\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{3}{2} u \omega_{1}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}-\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = \frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u-\frac{1}{2} \omega_{3} v-\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}-\frac{1}{2} u \omega_{1}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = -\frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- u^{2} \omega_{1}+\frac{1}{2} u \omega_{1}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{2} \omega_{3} v-\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{4} v^{2} \omega_{4}+\frac{1}{4} \omega_{4} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = -\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = -\frac{1}{2} v \omega_{0}-\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} v \omega_{2}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = -\frac{1}{2} v \omega_{4}-\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}-\frac{1}{2} \omega_{2}+\frac{3}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = -\frac{1}{2} v \omega_{0}+\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} v \omega_{2}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{3} v^{2}-\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{2} v \omega_{4}-\frac{1}{2} v \omega_{0}+\frac{1}{4} \omega_{3}+\frac{1}{4} \omega_{3} u^{2}- v^{2} \omega_{2}+\frac{1}{2} \omega_{2}-\frac{1}{2} v \omega_{2}+\frac{1}{4} \omega_{3} v^{2}+\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}+\frac{1}{4} v^{2} \omega_{4}-\frac{1}{4} \omega_{4} u^{2}+\frac{1}{2} v^{2} \omega_{0}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m6_matB.tex b/tex/d2q5/d2q5m6_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..b2833261c68e5c1e6e39a5af1d8719711160473a --- /dev/null +++ b/tex/d2q5/d2q5m6_matB.tex @@ -0,0 +1,9 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1-2 \omega_{3} u+\omega_{3}+2 u \omega_{1} & -1+\omega_{3}+2 v \omega_{2}-2 \omega_{3} v & -1+2 \omega_{3} u+\omega_{3}-2 u \omega_{1} & -1+\omega_{3}-2 v \omega_{2}+2 \omega_{3} v\\ + -1-\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+ u \omega_{1}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1} & 0 & -1-\frac{1}{2} v \omega_{4}-\frac{1}{2} \omega_{3} u+ u \omega_{1}-\frac{1}{2} \omega_{4} u+\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1- \omega_{3} u+2 u \omega_{1}- \omega_{4} u+\omega_{1} & -1+\frac{1}{2} v \omega_{4}-\frac{1}{2} \omega_{3} u+ u \omega_{1}-\frac{1}{2} \omega_{4} u-\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1-\frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}+ v \omega_{2}-\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4} & -1-\frac{1}{2} v \omega_{4}+\frac{1}{2} \omega_{3} u+\frac{1}{2} \omega_{2}+ v \omega_{2}-\frac{1}{2} \omega_{4} u-\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4} & 0 & -1-\frac{1}{2} v \omega_{4}-\frac{1}{2} \omega_{3} u+\frac{1}{2} \omega_{2}+ v \omega_{2}+\frac{1}{2} \omega_{4} u-\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4} & -1- v \omega_{4}+\omega_{2}+2 v \omega_{2}- \omega_{3} v\\ + -1+\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}- u \omega_{1}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1} & -1+ \omega_{3} u-2 u \omega_{1}+ \omega_{4} u+\omega_{1} & -1-\frac{1}{2} v \omega_{4}+\frac{1}{2} \omega_{3} u- u \omega_{1}+\frac{1}{2} \omega_{4} u+\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & 0 & -1+\frac{1}{2} v \omega_{4}+\frac{1}{2} \omega_{3} u- u \omega_{1}+\frac{1}{2} \omega_{4} u-\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}- v \omega_{2}+\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4} & -1+\frac{1}{2} v \omega_{4}+\frac{1}{2} \omega_{3} u+\frac{1}{2} \omega_{2}- v \omega_{2}-\frac{1}{2} \omega_{4} u+\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4} & -1+ v \omega_{4}+\omega_{2}-2 v \omega_{2}+ \omega_{3} v & -1+\frac{1}{2} v \omega_{4}-\frac{1}{2} \omega_{3} u+\frac{1}{2} \omega_{2}- v \omega_{2}+\frac{1}{2} \omega_{4} u+\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d2q5/d2q5m6_matB_per_els.tex b/tex/d2q5/d2q5m6_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..def36e63542ff7ec5d6099eac3570350cc1cddf4 --- /dev/null +++ b/tex/d2q5/d2q5m6_matB_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1-2 \omega_{3} u+\omega_{3}+2 u \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{3}+2 v \omega_{2}-2 \omega_{3} v, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+2 \omega_{3} u+\omega_{3}-2 u \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega_{3}-2 v \omega_{2}+2 \omega_{3} v, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1-\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}+ u \omega_{1}-\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1-\frac{1}{2} v \omega_{4}-\frac{1}{2} \omega_{3} u+ u \omega_{1}-\frac{1}{2} \omega_{4} u+\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1- \omega_{3} u+2 u \omega_{1}- \omega_{4} u+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\frac{1}{2} v \omega_{4}-\frac{1}{2} \omega_{3} u+ u \omega_{1}-\frac{1}{2} \omega_{4} u-\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1-\frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}+ v \omega_{2}-\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1-\frac{1}{2} v \omega_{4}+\frac{1}{2} \omega_{3} u+\frac{1}{2} \omega_{2}+ v \omega_{2}-\frac{1}{2} \omega_{4} u-\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1-\frac{1}{2} v \omega_{4}-\frac{1}{2} \omega_{3} u+\frac{1}{2} \omega_{2}+ v \omega_{2}+\frac{1}{2} \omega_{4} u-\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1- v \omega_{4}+\omega_{2}+2 v \omega_{2}- \omega_{3} v, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{2} \omega_{3} u+\frac{1}{4} \omega_{3}- u \omega_{1}+\frac{1}{2} \omega_{4} u+\frac{1}{4} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+ \omega_{3} u-2 u \omega_{1}+ \omega_{4} u+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1-\frac{1}{2} v \omega_{4}+\frac{1}{2} \omega_{3} u- u \omega_{1}+\frac{1}{2} \omega_{4} u+\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{2} v \omega_{4}+\frac{1}{2} \omega_{3} u- u \omega_{1}+\frac{1}{2} \omega_{4} u-\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{2} v \omega_{4}+\frac{1}{4} \omega_{3}+\frac{1}{2} \omega_{2}- v \omega_{2}+\frac{1}{2} \omega_{3} v+\frac{1}{4} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\frac{1}{2} v \omega_{4}+\frac{1}{2} \omega_{3} u+\frac{1}{2} \omega_{2}- v \omega_{2}-\frac{1}{2} \omega_{4} u+\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+ v \omega_{4}+\omega_{2}-2 v \omega_{2}+ \omega_{3} v, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{2} v \omega_{4}-\frac{1}{2} \omega_{3} u+\frac{1}{2} \omega_{2}- v \omega_{2}+\frac{1}{2} \omega_{4} u+\frac{1}{2} \omega_{3} v+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d2q5/d2q5m6_matK.tex b/tex/d2q5/d2q5m6_matK.tex new file mode 100644 index 0000000000000000000000000000000000000000..19d9dd3ad4450d3aefb5c1ef069930b50ec4febc --- /dev/null +++ b/tex/d2q5/d2q5m6_matK.tex @@ -0,0 +1,10 @@ +\noindent +\begin{equation*} +\matr{K} = \begin{pmatrix} + 1 &1 &1 &1 &1\\ + -u &1-u &-u &-u-1 &-u\\ + -v &-v &1-v &-v &-v-1\\ + v^2+u^2 &v^2+u^2-2u+1 &v^2-2v+u^2+1 &v^2+u^2+2u+1 &v^2+2v+u^2+1\\ + u^2-v^2 &-v^2+u^2-2u+1 &-v^2+2v+u^2-1 &-v^2+u^2+2u+1 &-v^2-2v+u^2-1 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d2q5/d2q5m6_matK_per_els.tex b/tex/d2q5/d2q5m6_matK_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..72d86748ebca4efd20983642c46c12660230fd90 --- /dev/null +++ b/tex/d2q5/d2q5m6_matK_per_els.tex @@ -0,0 +1,78 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{K}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,1} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,2} = 1-u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,3} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,4} = (-u)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,5} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,1} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,2} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,3} = 1-v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,4} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,5} = (-v)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,1} = v^2+u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,2} = v^2+u^2-2u+1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,3} = v^2-2v+u^2+1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,4} = v^2+u^2+2u+1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,5} = v^2+2v+u^2+1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,1} = u^2-v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,2} = (-v^2)+u^2-2u+1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,3} = (-v^2)+2v+u^2-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,4} = (-v^2)+u^2+2u+1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,5} = (-v^2)-2v+u^2-1. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d2q5/supp_d2q5_defs.tex b/tex/d2q5/supp_d2q5_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..2f6b657f208195f8650df8fcb06fb3cf3a7c4448 --- /dev/null +++ b/tex/d2q5/supp_d2q5_defs.tex @@ -0,0 +1,21 @@ +\section{Global definitions} +In $\mathbb{R}^2$, the position and velocity vectors are given by $\vx=(x,y)$ and $\vu=(u,v)$, respectively. +% Let +% \begin{align*} +% \phi_{k_1k_2}^\ell &:= \phi_{x+k_1\dl,y+k_2\dl}^{t+\ell\dt}=\phi(t-\ell\dt,(x+k_1\dl,y+k_2\dl)), +% \\ +% \left[ \psi \right]_{k_1k_2}^\ell &:= \psi(t-\ell\dt,(x+k_1\dl,y+k_2\dl)). +% \end{align*} +% Additionally, negative subscript numbers are denoted by $\bar n:=-n$, i.e., $\bar1:=-1$, $\bar2:=-2$, etc. +\noindent +\input{d2q5/d2q5_C} +\input{d2q5/d2q5m0_feq} +Lattice speed of sound: $c_s = \frac1{\sqrt{3}}$. + +\noindent +Moments $\vec{\mu} = \left( \mu_1, \mu_2, \dots, \mu_5 \right)^T$ are given by +$$ + \vec{\mu} = \matr{\hatM} \vec{f}, +$$ +where $\vec{f} = \left( f_1,f_2,\dots,f_5 \right)^T$ and +\input{d2q5/d2q5_matM} diff --git a/tex/d2q5/supp_d2q5m0_defs.tex b/tex/d2q5/supp_d2q5m0_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..d877f7d556c49d5585153648fc4065a3413cb17d --- /dev/null +++ b/tex/d2q5/supp_d2q5m0_defs.tex @@ -0,0 +1,11 @@ +\subsection{Definitions} +Matrix $\matr{A}=\matr{S}$: +\input{d2q5/d2q5m0_matA} +where +$$ + \matr{S} = \mathrm{diag}(\omega,\omega,\omega,\omega,\omega). +$$ + +\noindent +Matrix $\matr{B}$: +\input{d2q5/d2q5m0_matB} diff --git a/tex/d2q5/supp_d2q5m1_defs.tex b/tex/d2q5/supp_d2q5m1_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..36bc322992c194a2d348adbf46e7c64b8708c23a --- /dev/null +++ b/tex/d2q5/supp_d2q5m1_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d2q5/d2q5m1_matA} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4) +$$ +and +\input{d2q5/d2q5m1_matM} + +\noindent +Matrix $\matr{B}$: +\input{d2q5/d2q5m1_matB} diff --git a/tex/d2q5/supp_d2q5m2_defs.tex b/tex/d2q5/supp_d2q5m2_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..f780e520c377bdef3c0e7f8f661f3d3e280d9e45 --- /dev/null +++ b/tex/d2q5/supp_d2q5m2_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d2q5/d2q5m2_matA} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4) +$$ +and +\input{d2q5/d2q5m2_matM} + +\noindent +Matrix $\matr{B}$: +\input{d2q5/d2q5m2_matB} diff --git a/tex/d2q5/supp_d2q5m3_defs.tex b/tex/d2q5/supp_d2q5m3_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..f24f64de9fe78d5ab06a44ddbd26796d2e168b98 --- /dev/null +++ b/tex/d2q5/supp_d2q5m3_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d2q5/d2q5m3_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4) +$$ +and +\input{d2q5/d2q5m3_matM} + +\noindent +Matrix $\matr{B}$: +\input{d2q5/d2q5m3_matB} diff --git a/tex/d2q5/supp_d2q5m4_defs.tex b/tex/d2q5/supp_d2q5m4_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..5ce7d6db2ca0d32e44e8e1f01cafce710c57b3e8 --- /dev/null +++ b/tex/d2q5/supp_d2q5m4_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d2q5/d2q5m4_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4) +$$ +and +\input{d2q5/d2q5m4_matM} + +\noindent +Matrix $\matr{B}$: +\input{d2q5/d2q5m4_matB} diff --git a/tex/d2q5/supp_d2q5m5_defs.tex b/tex/d2q5/supp_d2q5m5_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..0854856ccfbf421951fa0007df4e10fe7bdda3d4 --- /dev/null +++ b/tex/d2q5/supp_d2q5m5_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{K}^{-1} \matr{S} \matr{K}$: +\input{d2q5/d2q5m5_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4) +$$ +and +\input{d2q5/d2q5m5_matK} + +\noindent +Matrix $\matr{B}$: +\input{d2q5/d2q5m5_matB_per_els} diff --git a/tex/d2q5/supp_d2q5m6_defs.tex b/tex/d2q5/supp_d2q5m6_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..207f0923bca99b57cbe337043d617f7fddf4a696 --- /dev/null +++ b/tex/d2q5/supp_d2q5m6_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{K}^{-1} \matr{S} \matr{K}$: +\input{d2q5/d2q5m6_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4) +$$ +and +\input{d2q5/d2q5m6_matK} + +\noindent +Matrix $\matr{B}$: +\input{d2q5/d2q5m6_matB_per_els} diff --git a/tex/d3q7/d3q7_C.tex b/tex/d3q7/d3q7_C.tex new file mode 100644 index 0000000000000000000000000000000000000000..007aa7e80d9d297b35109683278df4449402d013 --- /dev/null +++ b/tex/d3q7/d3q7_C.tex @@ -0,0 +1,14 @@ +Discrete velocity vectors: +\noindent +\begin{equation*} +\{ \vc_i \}_{i=1}^7 = +\left( + \colvec{3}{0}{0}{0}, + \colvec{3}{1}{0}{0}, + \colvec{3}{0}{1}{0}, + \colvec{3}{0}{0}{1}, + \colvec{3}{-1}{0}{0}, + \colvec{3}{0}{-1}{0}, + \colvec{3}{0}{0}{-1} +\right). +\end{equation*} diff --git a/tex/d3q7/d3q7_defs.tex b/tex/d3q7/d3q7_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..33ef306cde591a0af7be9e7126de7794cc1263be --- /dev/null +++ b/tex/d3q7/d3q7_defs.tex @@ -0,0 +1,14 @@ +\newcommand{\mA}{m_{000}} +\newcommand{\kA}{k_{000}} +\newcommand{\mB}{m_{100}} +\newcommand{\kB}{k_{100}} +\newcommand{\mC}{m_{010}} +\newcommand{\kC}{k_{010}} +\newcommand{\mD}{m_{001}} +\newcommand{\kD}{k_{001}} +\newcommand{\mE}{m_{200}} +\newcommand{\kE}{k_{200}} +\newcommand{\mF}{m_{020}} +\newcommand{\kF}{k_{020}} +\newcommand{\mG}{m_{002}} +\newcommand{\kG}{k_{002}} diff --git a/tex/d3q7/d3q7_matM.tex b/tex/d3q7/d3q7_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..a5e16547726deb5777ff1a373ddf6e3e3f5f6245 --- /dev/null +++ b/tex/d3q7/d3q7_matM.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{\hatM} = \begin{pmatrix} + 1 & 1 & 1 & 1 & 1 & 1 & 1\\ + 0 & 1 & 0 & 0 & -1 & 0 & 0\\ + 0 & 0 & 1 & 0 & 0 & -1 & 0\\ + 0 & 0 & 0 & 1 & 0 & 0 & -1\\ + 0 & 1 & 0 & 0 & 1 & 0 & 0\\ + 0 & 0 & 1 & 0 & 0 & 1 & 0\\ + 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7_matM_per_els.tex b/tex/d3q7/d3q7_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..707d67c21a6c9dddd438f62517da73e745706463 --- /dev/null +++ b/tex/d3q7/d3q7_matM_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{\hatM}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{4,7} = -1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{5,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{6,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{6,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{6,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{6,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{7,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{7,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{7,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{\hatM}_{7,7} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m0_feq.tex b/tex/d3q7/d3q7m0_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..c315a7868a27479d8ebc5d79be1571040758c602 --- /dev/null +++ b/tex/d3q7/d3q7m0_feq.tex @@ -0,0 +1,13 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-v^{2}-3 c_s^{2}-u^{2}-w^{2}\\ + \frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + \frac{1}{2} v^{2}+\frac{1}{2} v+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} w+\frac{1}{2} w^{2}\\ + -\frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + \frac{1}{2} v^{2}-\frac{1}{2} v+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} c_s^{2}-\frac{1}{2} w+\frac{1}{2} w^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m0_matA.tex b/tex/d3q7/d3q7m0_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..d9d30eb35ae7158fea2c6b352b443d7af52c66c4 --- /dev/null +++ b/tex/d3q7/d3q7m0_matA.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \omega & 0 & 0 & 0 & 0 & 0 & 0\\ + 0 & \omega & 0 & 0 & 0 & 0 & 0\\ + 0 & 0 & \omega & 0 & 0 & 0 & 0\\ + 0 & 0 & 0 & \omega & 0 & 0 & 0\\ + 0 & 0 & 0 & 0 & \omega & 0 & 0\\ + 0 & 0 & 0 & 0 & 0 & \omega & 0\\ + 0 & 0 & 0 & 0 & 0 & 0 & \omega\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m0_matA_per_els.tex b/tex/d3q7/d3q7m0_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..c1c7039845688ffa1ed03733792d91b1ff1b5207 --- /dev/null +++ b/tex/d3q7/d3q7m0_matA_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,6} = \omega, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,7} = \omega. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m0_matB.tex b/tex/d3q7/d3q7m0_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..97640fe7d132760cad23a6474bb961b4700e9845 --- /dev/null +++ b/tex/d3q7/d3q7m0_matB.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & \omega-1 & \omega-1 & \omega-1 & \omega-1 & \omega-1 & \omega-1\\ + \omega-1 & 0 & \omega-1 & \omega-1 & \omega-1 & \omega-1 & \omega-1\\ + \omega-1 & \omega-1 & 0 & \omega-1 & \omega-1 & \omega-1 & \omega-1\\ + \omega-1 & \omega-1 & \omega-1 & 0 & \omega-1 & \omega-1 & \omega-1\\ + \omega-1 & \omega-1 & \omega-1 & \omega-1 & 0 & \omega-1 & \omega-1\\ + \omega-1 & \omega-1 & \omega-1 & \omega-1 & \omega-1 & 0 & \omega-1\\ + \omega-1 & \omega-1 & \omega-1 & \omega-1 & \omega-1 & \omega-1 & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m0_matB_per_els.tex b/tex/d3q7/d3q7m0_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..41114766d0cb33387918513c5ca8dc5665b81f0a --- /dev/null +++ b/tex/d3q7/d3q7m0_matB_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,6} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,7} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,6} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,7} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,6} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,7} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,6} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,7} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,6} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,7} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,1} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,2} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,3} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,4} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,5} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,7} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,1} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,2} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,3} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,4} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,5} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,6} = \omega-1, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,7} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m0_matM.tex b/tex/d3q7/d3q7m0_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..cb2a3b19e51131fafa2b9ca4f7be6a590648652e --- /dev/null +++ b/tex/d3q7/d3q7m0_matM.tex @@ -0,0 +1,12 @@ +Matrix $\matr{M}$: +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 & 1 & 1 & 1 & 1 & 1 & 1\\ + 0 & 1 & 0 & 0 & -1 & 0 & 0\\ + 0 & 0 & 1 & 0 & 0 & -1 & 0\\ + 0 & 0 & 0 & 1 & 0 & 0 & -1\\ + 0 & 1 & 0 & 0 & 1 & 0 & 0\\ + 0 & 0 & 1 & 0 & 0 & 1 & 0\\ + 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m0_matM_per_els.tex b/tex/d3q7/d3q7m0_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..10b51a7a2a31c91d8ea6af3dc7fdaf460d18f212 --- /dev/null +++ b/tex/d3q7/d3q7m0_matM_per_els.tex @@ -0,0 +1,151 @@ +Matrix $\matr{M}$: +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,7} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,7} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m1_feq.tex b/tex/d3q7/d3q7m1_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..191593578c9ab50a8a8ccd5910e7138c0638e160 --- /dev/null +++ b/tex/d3q7/d3q7m1_feq.tex @@ -0,0 +1,13 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-v^{2}-3 c_s^{2}-u^{2}-w^{2}\\ + \frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + \frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}+\frac{1}{2} v\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} w+\frac{1}{2} w^{2}\\ + -\frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + \frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}-\frac{1}{2} v\\ + \frac{1}{2} c_s^{2}-\frac{1}{2} w+\frac{1}{2} w^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m1_matA.tex b/tex/d3q7/d3q7m1_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..78243e1d496f01d72ba79fdc92419e69dda455a8 --- /dev/null +++ b/tex/d3q7/d3q7m1_matA.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + -\omega_{6}+\omega_{0} & 0 & 0 & 0 & 0 & 0 & 0\\ + 0 & \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{4} & 0 & 0 & -\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{4} & 0 & 0\\ + 0 & 0 & \frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & 0 & \frac{1}{2} \omega_{5}-\frac{1}{2} \omega_{2} & 0\\ + 0 & 0 & 0 & \frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & 0 & 0 & \frac{1}{2} \omega_{6}-\frac{1}{2} \omega_{3}\\ + 0 & -\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{4} & 0 & 0 & \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{4} & 0 & 0\\ + 0 & 0 & \frac{1}{2} \omega_{5}-\frac{1}{2} \omega_{2} & 0 & 0 & \frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & 0\\ + 0 & 0 & 0 & \frac{1}{2} \omega_{6}-\frac{1}{2} \omega_{3} & 0 & 0 & \frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m1_matA_per_els.tex b/tex/d3q7/d3q7m1_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..438434aab9a21b73e9f8f2ec90ffc07af69873ed --- /dev/null +++ b/tex/d3q7/d3q7m1_matA_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = -\omega_{6}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = -\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,6} = \frac{1}{2} \omega_{5}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,7} = \frac{1}{2} \omega_{6}-\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = -\frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,3} = \frac{1}{2} \omega_{5}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,6} = \frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,4} = \frac{1}{2} \omega_{6}-\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,7} = \frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m1_matB.tex b/tex/d3q7/d3q7m1_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..21e1f04fd91e2b6191dd89b00d6ab9c9b312e42c --- /dev/null +++ b/tex/d3q7/d3q7m1_matB.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega_{4} & -1+\omega_{5} & -1+\omega_{6} & -1+\omega_{4} & -1+\omega_{5} & -1+\omega_{6}\\ + -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}\\ + -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & 0 & -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\omega_{3}\\ + -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}\\ + -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\omega_{3} & -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m1_matB_per_els.tex b/tex/d3q7/d3q7m1_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..391e2c1655acae38c2e8c8954447bf4f06aa2d72 --- /dev/null +++ b/tex/d3q7/d3q7m1_matB_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,6} = -1+\omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,7} = -1+\omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,6} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,7} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,6} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,7} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,6} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,7} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,6} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,7} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,1} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,2} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,4} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,5} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,7} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,1} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,2} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,3} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,4} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,5} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,6} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,7} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m1_matM.tex b/tex/d3q7/d3q7m1_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..b75b6366c4062299ba94a91b8e517812b8b28d88 --- /dev/null +++ b/tex/d3q7/d3q7m1_matM.tex @@ -0,0 +1,12 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 &1 &1 &1 &1 &1 &1\\ + 0 &1 &0 &0 &-1 &0 &0\\ + 0 &0 &1 &0 &0 &-1 &0\\ + 0 &0 &0 &1 &0 &0 &-1\\ + 0 &1 &0 &0 &1 &0 &0\\ + 0 &0 &1 &0 &0 &1 &0\\ + 0 &0 &0 &1 &0 &0 &1 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m1_matM_per_els.tex b/tex/d3q7/d3q7m1_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..cdfc6790bc01e985cd3c7624f23d4f65ee640bdc --- /dev/null +++ b/tex/d3q7/d3q7m1_matM_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,7} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,7} = 1. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m2_feq.tex b/tex/d3q7/d3q7m2_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..61cc40c3101f0dcb02a6da58981d0e7f29dc9889 --- /dev/null +++ b/tex/d3q7/d3q7m2_feq.tex @@ -0,0 +1,13 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-u^{2}-v^{2}-3 c_s^{2}-w^{2}\\ + \frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}+\frac{1}{2} u\\ + \frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}+\frac{1}{2} v\\ + \frac{1}{2} w+\frac{1}{2} c_s^{2}+\frac{1}{2} w^{2}\\ + \frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}-\frac{1}{2} u\\ + \frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}-\frac{1}{2} v\\ + -\frac{1}{2} w+\frac{1}{2} c_s^{2}+\frac{1}{2} w^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m2_matA.tex b/tex/d3q7/d3q7m2_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..2e96eea6d5b6d3c03f8befbf95a4b1a42b679cd0 --- /dev/null +++ b/tex/d3q7/d3q7m2_matA.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \omega_{0} & -\omega_{4}+\omega_{0} & -\omega_{4}+\omega_{0} & -\omega_{4}+\omega_{0} & -\omega_{4}+\omega_{0} & -\omega_{4}+\omega_{0} & -\omega_{4}+\omega_{0}\\ + 0 & \frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6} & \frac{1}{6} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}\\ + 0 & \frac{1}{6} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{5} & \frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6} & \frac{1}{6} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{5} & -\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}\\ + 0 & \frac{1}{6} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3} & \frac{1}{6} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{2} \omega_{3}\\ + 0 & \frac{1}{6} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6} & \frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}\\ + 0 & \frac{1}{6} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{5} & -\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6} & \frac{1}{6} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{5} & \frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}\\ + 0 & \frac{1}{6} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{2} \omega_{3} & \frac{1}{6} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5} & \frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m2_matA_per_els.tex b/tex/d3q7/d3q7m2_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..d710c5c15d884a4fe3089636c73ed32047575cb9 --- /dev/null +++ b/tex/d3q7/d3q7m2_matA_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -\omega_{4}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -\omega_{4}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = -\omega_{4}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = -\omega_{4}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,6} = -\omega_{4}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,7} = -\omega_{4}+\omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = \frac{1}{6} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,6} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,7} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = \frac{1}{6} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = \frac{1}{6} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,6} = -\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,7} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = \frac{1}{6} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = \frac{1}{6} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,6} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,7} = \frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = \frac{1}{6} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,6} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,7} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,2} = \frac{1}{6} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,3} = -\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,4} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,5} = \frac{1}{6} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,6} = \frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,7} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,2} = \frac{1}{6} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,3} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,4} = \frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,5} = \frac{1}{6} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,6} = \frac{1}{6} \omega_{4}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,7} = \frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m2_matB.tex b/tex/d3q7/d3q7m2_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..bd24bdf62b3b91cb441491cdcb0ecbb306440b73 --- /dev/null +++ b/tex/d3q7/d3q7m2_matB.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega_{4} & -1+\omega_{4} & -1+\omega_{4} & -1+\omega_{4} & -1+\omega_{4} & -1+\omega_{4}\\ + -1+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5} & 0 & -1+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5} & -1+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5} & -1+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}\\ + -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2} & -1-\frac{1}{6} \omega_{6}+\frac{2}{3} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2} & -1-\frac{1}{6} \omega_{6}+\frac{2}{3} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}\\ + -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{2}{3} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{6} \omega_{5} & -1+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{5} & 0 & -1+\frac{2}{3} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{6} \omega_{5} & -1+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{5} & -1+\omega_{3}\\ + -1+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5} & -1+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5} & 0 & -1+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5} & -1+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}\\ + -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2} & -1-\frac{1}{6} \omega_{6}+\frac{2}{3} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2} & -1-\frac{1}{6} \omega_{6}+\frac{2}{3} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}\\ + -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{2}{3} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{6} \omega_{5} & -1+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{5} & -1+\omega_{3} & -1+\frac{2}{3} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{6} \omega_{5} & -1+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{5} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m2_matB_per_els.tex b/tex/d3q7/d3q7m2_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..ab9b7aac5ae7ccf6b6f7873c8ac9911411ef681a --- /dev/null +++ b/tex/d3q7/d3q7m2_matB_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,6} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,7} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,6} = -1+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,7} = -1+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1-\frac{1}{6} \omega_{6}+\frac{2}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1-\frac{1}{6} \omega_{6}+\frac{2}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,6} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,7} = -1+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\frac{2}{3} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{2}{3} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,6} = -1+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,7} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,6} = -1+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,7} = -1+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,1} = -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,2} = -1-\frac{1}{6} \omega_{6}+\frac{2}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,4} = -1+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,5} = -1-\frac{1}{6} \omega_{6}+\frac{2}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,7} = -1+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,1} = -1+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,2} = -1+\frac{2}{3} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,3} = -1+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,4} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,5} = -1+\frac{2}{3} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,6} = -1+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,7} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m2_matM.tex b/tex/d3q7/d3q7m2_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..1ef7774d60d302c2a0141a342cb9b7e47a476765 --- /dev/null +++ b/tex/d3q7/d3q7m2_matM.tex @@ -0,0 +1,12 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 &1 &1 &1 &1 &1 &1\\ + 0 &1 &0 &0 &-1 &0 &0\\ + 0 &0 &1 &0 &0 &-1 &0\\ + 0 &0 &0 &1 &0 &0 &-1\\ + 0 &1 &1 &1 &1 &1 &1\\ + 0 &1 &-1 &0 &1 &-1 &0\\ + 0 &1 &0 &-1 &1 &0 &-1 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m2_matM_per_els.tex b/tex/d3q7/d3q7m2_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..d17b0b7b567d28914d97b5dc5d6945466eeb5d87 --- /dev/null +++ b/tex/d3q7/d3q7m2_matM_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,7} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,3} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,4} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,7} = -1. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m3_feq.tex b/tex/d3q7/d3q7m3_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..1cfaa38231e0107bfa5814517716d877824930fa --- /dev/null +++ b/tex/d3q7/d3q7m3_feq.tex @@ -0,0 +1,13 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-v^{2}-u^{2}-w^{2}-3 c_s^{2}\\ + \frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}+\frac{1}{2} u\\ + \frac{1}{2} v^{2}+\frac{1}{2} v+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} w+\frac{1}{2} w^{2}+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}-\frac{1}{2} u\\ + \frac{1}{2} v^{2}-\frac{1}{2} v+\frac{1}{2} c_s^{2}\\ + -\frac{1}{2} w+\frac{1}{2} w^{2}+\frac{1}{2} c_s^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m3_matA.tex b/tex/d3q7/d3q7m3_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..489db9e3b937195337b6ae893cfc5f053741002d --- /dev/null +++ b/tex/d3q7/d3q7m3_matA.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{2}{3} \omega_{6}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{5}{14} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{5}{14} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{3}{10} \omega_{5}-\frac{1}{2} \omega_{2}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}\\ + \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{5}{14} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{5}{14} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{3}{10} \omega_{5}-\frac{1}{2} \omega_{2}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}\\ + \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m3_matA_per_els.tex b/tex/d3q7/d3q7m3_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..25aa998e7f2b0b40385fa07420b78cf43349e5da --- /dev/null +++ b/tex/d3q7/d3q7m3_matA_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{2}{3} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,6} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,7} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{5}{14} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = \frac{5}{14} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,6} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,7} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,6} = \frac{3}{10} \omega_{5}-\frac{1}{2} \omega_{2}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,7} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,6} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,7} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = \frac{5}{14} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{5}{14} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,6} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,7} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,1} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,2} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,3} = \frac{3}{10} \omega_{5}-\frac{1}{2} \omega_{2}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,4} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,5} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,6} = \frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,7} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,1} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}-\frac{1}{3} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,2} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,3} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,4} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{6} \omega_{6}-\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,5} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,6} = -\frac{1}{5} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,7} = \frac{2}{15} \omega_{5}+\frac{2}{35} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m3_matB.tex b/tex/d3q7/d3q7m3_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..55556d83325cc85e83ae75d6c1c4f7934a0597c8 --- /dev/null +++ b/tex/d3q7/d3q7m3_matB.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\frac{1}{5} \omega_{4}+\frac{2}{3} \omega_{6}+\frac{2}{15} \omega_{5} & -1+\frac{2}{3} \omega_{6}+\frac{1}{3} \omega_{5} & -1+\omega_{6} & -1+\frac{1}{5} \omega_{4}+\frac{2}{3} \omega_{6}+\frac{2}{15} \omega_{5} & -1+\frac{2}{3} \omega_{6}+\frac{1}{3} \omega_{5} & -1+\omega_{6}\\ + -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\frac{1}{5} \omega_{4}+\frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\frac{1}{5} \omega_{4}+\frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}\\ + -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{1}{5} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{2}{15} \omega_{5} & -1+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{3} \omega_{5} & 0 & -1+\frac{1}{5} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{2}{15} \omega_{5} & -1+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{3} \omega_{5} & -1+\omega_{3}\\ + -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & 0 & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1} & -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}\\ + -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\frac{1}{5} \omega_{4}+\frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\frac{1}{5} \omega_{4}+\frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}\\ + -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3} & -1+\frac{1}{5} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{2}{15} \omega_{5} & -1+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{3} \omega_{5} & -1+\omega_{3} & -1+\frac{1}{5} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{2}{15} \omega_{5} & -1+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{3} \omega_{5} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m3_matB_per_els.tex b/tex/d3q7/d3q7m3_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..ee075a1ff35174c81b24be12649a8c6c4f60cad5 --- /dev/null +++ b/tex/d3q7/d3q7m3_matB_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\frac{1}{5} \omega_{4}+\frac{2}{3} \omega_{6}+\frac{2}{15} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\frac{2}{3} \omega_{6}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\frac{1}{5} \omega_{4}+\frac{2}{3} \omega_{6}+\frac{2}{15} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,6} = -1+\frac{2}{3} \omega_{6}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,7} = -1+\omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,6} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,7} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{1}{5} \omega_{4}+\frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\frac{1}{5} \omega_{4}+\frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,6} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,7} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\frac{1}{5} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{2}{15} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{5} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{2}{15} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,6} = -1+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,7} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,6} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,7} = -1+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,1} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,2} = -1+\frac{1}{5} \omega_{4}+\frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,4} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,5} = -1+\frac{1}{5} \omega_{4}+\frac{3}{10} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,7} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,1} = -1+\frac{1}{2} \omega_{6}+\frac{1}{2} \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,2} = -1+\frac{1}{5} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{2}{15} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,3} = -1+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,4} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,5} = -1+\frac{1}{5} \omega_{4}+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{2}{15} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,6} = -1+\frac{1}{6} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{3} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,7} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m3_matM.tex b/tex/d3q7/d3q7m3_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..acc095c936e3fced569abced8dceb0fa7cdb7156 --- /dev/null +++ b/tex/d3q7/d3q7m3_matM.tex @@ -0,0 +1,12 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 &1 &1 &1 &1 &1 &1\\ + 0 &1 &0 &0 &-1 &0 &0\\ + 0 &0 &1 &0 &0 &-1 &0\\ + 0 &0 &0 &1 &0 &0 &-1\\ + -2 &5 &-2 &-2 &5 &-2 &-2\\ + -2 &0 &3 &-2 &0 &3 &-2\\ + -2 &0 &0 &1 &0 &0 &1 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m3_matM_per_els.tex b/tex/d3q7/d3q7m3_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..b2519a8a637433775e5e001915c99b9d80c1ab74 --- /dev/null +++ b/tex/d3q7/d3q7m3_matM_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,7} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 5, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 5, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,6} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,7} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,1} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,3} = 3, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,4} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,6} = 3, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,7} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,1} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,7} = 1. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m4_feq.tex b/tex/d3q7/d3q7m4_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..73ab3a2dcd7d8c2c8e6d291ce02ca9e9ce606193 --- /dev/null +++ b/tex/d3q7/d3q7m4_feq.tex @@ -0,0 +1,13 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-v^{2}-3 c_s^{2}-u^{2}-w^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}+\frac{1}{2} u\\ + \frac{1}{2} v^{2}+\frac{1}{2} v+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} w+\frac{1}{2} w^{2}\\ + \frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}-\frac{1}{2} u\\ + \frac{1}{2} v^{2}-\frac{1}{2} v+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} c_s^{2}-\frac{1}{2} w+\frac{1}{2} w^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m4_matA.tex b/tex/d3q7/d3q7m4_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..d659ae38c771ef5a9a75b9723729ef0789f9ffb0 --- /dev/null +++ b/tex/d3q7/d3q7m4_matA.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + \frac{6}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}-\frac{1}{2} \omega_{2} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}-\frac{1}{2} \omega_{2} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5} & \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}\\ + -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0} & \frac{1}{42} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m4_matA_per_els.tex b/tex/d3q7/d3q7m4_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..dfc8ec60c7a51b7a54faf1a4d7b4aab31a72c3e7 --- /dev/null +++ b/tex/d3q7/d3q7m4_matA_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = \frac{6}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,6} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,7} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{42} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = \frac{1}{42} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,6} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,7} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,6} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,7} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{42} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,6} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,7} = \frac{1}{42} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = \frac{1}{42} \omega_{4}-\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{42} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,6} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,7} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,1} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,2} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,3} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,4} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,5} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}-\frac{1}{4} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,6} = \frac{1}{42} \omega_{4}+\frac{1}{12} \omega_{6}+\frac{1}{7} \omega_{0}+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,7} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,1} = -\frac{1}{7} \omega_{4}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,2} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,3} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,4} = \frac{1}{42} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,5} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,6} = \frac{1}{42} \omega_{4}-\frac{1}{6} \omega_{6}+\frac{1}{7} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,7} = \frac{1}{42} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{7} \omega_{0}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m4_matB.tex b/tex/d3q7/d3q7m4_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..40cdb56d67e4626a2246a5ce586905ca0e36be3f --- /dev/null +++ b/tex/d3q7/d3q7m4_matB.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+\omega_{4} & -1+\omega_{4} & -1+\omega_{4} & -1+\omega_{4} & -1+\omega_{4} & -1+\omega_{4}\\ + -1+\frac{1}{4} \omega_{5}+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6} & 0 & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{1} & -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{6} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{1} & -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{6}\\ + -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{12} \omega_{6} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{4} \omega_{6} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{4} \omega_{6}\\ + -1+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6} & -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6} & -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6} & 0 & -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6} & -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6} & -1+\omega_{3}\\ + -1+\frac{1}{4} \omega_{5}+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6} & -1+\omega_{1} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{1} & -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{6} & 0 & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{1} & -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{6}\\ + -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{12} \omega_{6} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & -1+\omega_{2} & -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{4} \omega_{6} & -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2} & 0 & -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{4} \omega_{6}\\ + -1+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6} & -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6} & -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6} & -1+\omega_{3} & -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6} & -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m4_matB_per_els.tex b/tex/d3q7/d3q7m4_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..ca3b409e2559d34cb864b31741baae1363c2437d --- /dev/null +++ b/tex/d3q7/d3q7m4_matB_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,6} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,7} = -1+\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{4} \omega_{5}+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,6} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,7} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{12} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{4} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,6} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,7} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{4} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,6} = -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,7} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{4} \omega_{5}+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{12} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1+\omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,6} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{1}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,7} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{1}+\frac{1}{4} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,1} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+\frac{1}{12} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,2} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,3} = -1+\omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,4} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{4} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,5} = -1+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,7} = -1+\frac{1}{4} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{4} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,1} = -1+\frac{1}{2} \omega_{3}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,2} = -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,3} = -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,4} = -1+\omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,5} = -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,6} = -1+\frac{1}{2} \omega_{3}+\frac{1}{2} \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,7} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m4_matM.tex b/tex/d3q7/d3q7m4_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..a2ef6b9e460df2c63cd5ee6d1fac0043ee260c28 --- /dev/null +++ b/tex/d3q7/d3q7m4_matM.tex @@ -0,0 +1,12 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 &1 &1 &1 &1 &1 &1\\ + 0 &1 &0 &0 &-1 &0 &0\\ + 0 &0 &1 &0 &0 &-1 &0\\ + 0 &0 &0 &1 &0 &0 &-1\\ + -6 &1 &1 &1 &1 &1 &1\\ + 0 &1 &-1 &0 &1 &-1 &0\\ + 0 &1 &1 &-2 &1 &1 &-2 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m4_matM_per_els.tex b/tex/d3q7/d3q7m4_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..12d65803ee093fbb2a532426b9b93e27780b0dad --- /dev/null +++ b/tex/d3q7/d3q7m4_matM_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,7} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = -6, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,3} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,4} = -2, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,7} = -2. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m5_feq.tex b/tex/d3q7/d3q7m5_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..f307696c52a8345213e393245fb7de297e594abc --- /dev/null +++ b/tex/d3q7/d3q7m5_feq.tex @@ -0,0 +1,13 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-w^{2}-u^{2}-3 c_s^{2}-v^{2}\\ + \frac{1}{2} u+\frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} v+\frac{1}{2} c_s^{2}+\frac{1}{2} v^{2}\\ + \frac{1}{2} w^{2}+\frac{1}{2} c_s^{2}+\frac{1}{2} w\\ + -\frac{1}{2} u+\frac{1}{2} u^{2}+\frac{1}{2} c_s^{2}\\ + -\frac{1}{2} v+\frac{1}{2} c_s^{2}+\frac{1}{2} v^{2}\\ + \frac{1}{2} w^{2}+\frac{1}{2} c_s^{2}-\frac{1}{2} w +\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m5_matA.tex b/tex/d3q7/d3q7m5_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..4686f91a456b4ca9f916453fad910bb1ce0fbc53 --- /dev/null +++ b/tex/d3q7/d3q7m5_matA.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + - \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 \omega_{1} u^{2}- \omega_{5} v^{2} & - \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 u \omega_{4}+2 \omega_{1} u^{2}-2 \omega_{1} u- \omega_{5} v^{2}-\omega_{4} & -2 \omega_{2} v- \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 \omega_{5} v-\omega_{5}+2 \omega_{1} u^{2}- \omega_{5} v^{2} & - \omega_{0} u^{2}-\omega_{6}- w^{2} \omega_{0}- w^{2} \omega_{6}-2 w \omega_{3}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 \omega_{1} u^{2}+2 w \omega_{6}- \omega_{5} v^{2} & - \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}-2 u \omega_{4}+2 \omega_{1} u^{2}+2 \omega_{1} u- \omega_{5} v^{2}-\omega_{4} & 2 \omega_{2} v- \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}-2 \omega_{5} v-\omega_{5}+2 \omega_{1} u^{2}- \omega_{5} v^{2} & - \omega_{0} u^{2}-\omega_{6}- w^{2} \omega_{0}- w^{2} \omega_{6}+2 w \omega_{3}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 \omega_{1} u^{2}-2 w \omega_{6}- \omega_{5} v^{2}\\ + -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u & \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{0} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{2} u^{2} \omega_{4}- u \omega_{4}- \omega_{1} u^{2}+\frac{1}{2} \omega_{1} u+\frac{1}{2} \omega_{4} & -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u & -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u & -\frac{1}{2} {(1+u)} {( \omega_{1} {(1+2 u)}- \omega_{0} u- u \omega_{4}-\omega_{4})} & -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u & -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u\\ + -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v & -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v & \frac{1}{2} \omega_{2} v- \omega_{2} v^{2}+\frac{1}{2} \omega_{0} v^{2}- \omega_{5} v+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{5} v^{2}+\frac{1}{2} \omega_{0} v & -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v & -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v & \frac{1}{2} {(1+v)} {( {(1+v)} \omega_{5}- \omega_{2} {(1+2 v)}+ \omega_{0} v)} & -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v\\ + -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})} & -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})} & -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})} & \frac{1}{2} \omega_{6}+\frac{1}{2} w^{2} \omega_{0}+\frac{1}{2} w^{2} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{2} w \omega_{3}- w^{2} \omega_{3}- w \omega_{6}+\frac{1}{2} w \omega_{0} & -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})} & -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})} & \frac{1}{2} {( \omega_{6} {(1+w)}-\omega_{3}- w {(2 \omega_{3}-\omega_{0})})} {(1+w)}\\ + \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})} & \frac{1}{2} {( \omega_{0} u+ u \omega_{4}- \omega_{1} {(-1+2 u)}-\omega_{4})} {(-1+u)} & \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})} & \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})} & \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{2} u^{2} \omega_{4}+ u \omega_{4}- \omega_{1} u^{2}-\frac{1}{2} \omega_{1} u+\frac{1}{2} \omega_{4} & \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})} & \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})}\\ + \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v & \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v & \frac{1}{2} {( {(-1+v)} \omega_{5}- {(-1+2 v)} \omega_{2}+ \omega_{0} v)} {(-1+v)} & \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v & \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v & -\frac{1}{2} \omega_{2} v- \omega_{2} v^{2}+\frac{1}{2} \omega_{0} v^{2}+ \omega_{5} v+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{5} v^{2}-\frac{1}{2} \omega_{0} v & \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v\\ + 0 & \frac{1}{2} {(\omega_{3}-\omega_{0}- w {(2 \omega_{3}-\omega_{0})}+ w \omega_{6})} w & \frac{1}{2} {(\omega_{3}-\omega_{0}- w {(2 \omega_{3}-\omega_{0})}+ w \omega_{6})} w & \frac{1}{2} {(-1+w)} {(\omega_{3}- w {(2 \omega_{3}-\omega_{0})}+ \omega_{6} {(-1+w)})} & \frac{1}{2} {(\omega_{3}-\omega_{0}- w {(2 \omega_{3}-\omega_{0})}+ w \omega_{6})} w & \frac{1}{2} {(\omega_{3}-\omega_{0}- w {(2 \omega_{3}-\omega_{0})}+ w \omega_{6})} w & \frac{1}{2} \omega_{6}+\frac{1}{2} w^{2} \omega_{0}+\frac{1}{2} w^{2} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{2} w \omega_{3}- w^{2} \omega_{3}+ w \omega_{6}-\frac{1}{2} w \omega_{0}\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m5_matA_per_els.tex b/tex/d3q7/d3q7m5_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..dfb85fa2f7cc477a2b5ac672d6eaa0edf88ea92d --- /dev/null +++ b/tex/d3q7/d3q7m5_matA_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = - \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 \omega_{1} u^{2}- \omega_{5} v^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = - \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 u \omega_{4}+2 \omega_{1} u^{2}-2 \omega_{1} u- \omega_{5} v^{2}-\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -2 \omega_{2} v- \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 \omega_{5} v-\omega_{5}+2 \omega_{1} u^{2}- \omega_{5} v^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = - \omega_{0} u^{2}-\omega_{6}- w^{2} \omega_{0}- w^{2} \omega_{6}-2 w \omega_{3}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 \omega_{1} u^{2}+2 w \omega_{6}- \omega_{5} v^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = - \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}-2 u \omega_{4}+2 \omega_{1} u^{2}+2 \omega_{1} u- \omega_{5} v^{2}-\omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,6} = 2 \omega_{2} v- \omega_{0} u^{2}- w^{2} \omega_{0}- w^{2} \omega_{6}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}-2 \omega_{5} v-\omega_{5}+2 \omega_{1} u^{2}- \omega_{5} v^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,7} = - \omega_{0} u^{2}-\omega_{6}- w^{2} \omega_{0}- w^{2} \omega_{6}+2 w \omega_{3}- u^{2} \omega_{4}+2 \omega_{2} v^{2}+\omega_{0}+2 w^{2} \omega_{3}- \omega_{0} v^{2}+2 \omega_{1} u^{2}-2 w \omega_{6}- \omega_{5} v^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{0} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{2} u^{2} \omega_{4}- u \omega_{4}- \omega_{1} u^{2}+\frac{1}{2} \omega_{1} u+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = -\frac{1}{2} {(1+u)} {( \omega_{1} {(1+2 u)}- \omega_{0} u- u \omega_{4}-\omega_{4})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,6} = -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,7} = -\frac{1}{2} {( \omega_{1} {(1+2 u)}- u \omega_{4}- {(1+u)} \omega_{0})} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{2} \omega_{2} v- \omega_{2} v^{2}+\frac{1}{2} \omega_{0} v^{2}- \omega_{5} v+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{5} v^{2}+\frac{1}{2} \omega_{0} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,6} = \frac{1}{2} {(1+v)} {( {(1+v)} \omega_{5}- \omega_{2} {(1+2 v)}+ \omega_{0} v)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,7} = -\frac{1}{2} {( \omega_{2} {(1+2 v)}- \omega_{0} {(1+v)}- \omega_{5} v)} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = \frac{1}{2} \omega_{6}+\frac{1}{2} w^{2} \omega_{0}+\frac{1}{2} w^{2} \omega_{6}+\frac{1}{2} \omega_{3}+\frac{1}{2} w \omega_{3}- w^{2} \omega_{3}- w \omega_{6}+\frac{1}{2} w \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,6} = -\frac{1}{2} w {(\omega_{3}-\omega_{0}+ w {(2 \omega_{3}-\omega_{0})}- w \omega_{6})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,7} = \frac{1}{2} {( \omega_{6} {(1+w)}-\omega_{3}- w {(2 \omega_{3}-\omega_{0})})} {(1+w)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = \frac{1}{2} {( \omega_{0} u+ u \omega_{4}- \omega_{1} {(-1+2 u)}-\omega_{4})} {(-1+u)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = \frac{1}{2} \omega_{1}+\frac{1}{2} \omega_{0} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{2} u^{2} \omega_{4}+ u \omega_{4}- \omega_{1} u^{2}-\frac{1}{2} \omega_{1} u+\frac{1}{2} \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,6} = \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,7} = \frac{1}{2} u {( u \omega_{4}+ \omega_{0} {(-1+u)}- \omega_{1} {(-1+2 u)})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,1} = \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,2} = \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,3} = \frac{1}{2} {( {(-1+v)} \omega_{5}- {(-1+2 v)} \omega_{2}+ \omega_{0} v)} {(-1+v)}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,4} = \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,5} = \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,6} = -\frac{1}{2} \omega_{2} v- \omega_{2} v^{2}+\frac{1}{2} \omega_{0} v^{2}+ \omega_{5} v+\frac{1}{2} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{2} \omega_{5} v^{2}-\frac{1}{2} \omega_{0} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,7} = \frac{1}{2} {( {(-1+v)} \omega_{0}+ \omega_{5} v- {(-1+2 v)} \omega_{2})} v, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,2} = \frac{1}{2} {(\omega_{3}-\omega_{0}- w {(2 \omega_{3}-\omega_{0})}+ w \omega_{6})} w, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,3} = \frac{1}{2} {(\omega_{3}-\omega_{0}- w {(2 \omega_{3}-\omega_{0})}+ w \omega_{6})} w, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,4} = \frac{1}{2} {(-1+w)} {(\omega_{3}- w {(2 \omega_{3}-\omega_{0})}+ \omega_{6} {(-1+w)})}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,5} = \frac{1}{2} {(\omega_{3}-\omega_{0}- w {(2 \omega_{3}-\omega_{0})}+ w \omega_{6})} w, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,6} = \frac{1}{2} {(\omega_{3}-\omega_{0}- w {(2 \omega_{3}-\omega_{0})}+ w \omega_{6})} w, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,7} = \frac{1}{2} \omega_{6}+\frac{1}{2} w^{2} \omega_{0}+\frac{1}{2} w^{2} \omega_{6}+\frac{1}{2} \omega_{3}-\frac{1}{2} w \omega_{3}- w^{2} \omega_{3}+ w \omega_{6}-\frac{1}{2} w \omega_{0}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m5_matB.tex b/tex/d3q7/d3q7m5_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..4b5836b648d01e24e53030ccf1275bcb0945cd20 --- /dev/null +++ b/tex/d3q7/d3q7m5_matB.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+2 \omega_{1} u+\omega_{4}-2 \omega_{4} u & -1-2 v \omega_{5}+2 \omega_{2} v+\omega_{5} & -1+\omega_{6}+2 w \omega_{3}-2 w \omega_{6} & -1-2 \omega_{1} u+\omega_{4}+2 \omega_{4} u & -1+2 v \omega_{5}-2 \omega_{2} v+\omega_{5} & -1+\omega_{6}-2 w \omega_{3}+2 w \omega_{6}\\ + -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u & 0 & -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u & -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u & -1+2 \omega_{1} u+\omega_{1}-2 \omega_{4} u & -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u & -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u\\ + -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5} & -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5} & 0 & -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5} & -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5} & -1+\omega_{2}-2 v \omega_{5}+2 \omega_{2} v & -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5}\\ + -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6} & -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6} & -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6} & 0 & -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6} & -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6} & -1+2 w \omega_{3}+\omega_{3}-2 w \omega_{6}\\ + -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u & -1-2 \omega_{1} u+\omega_{1}+2 \omega_{4} u & -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u & -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u & 0 & -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u & -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u\\ + -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5} & -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5} & -1+\omega_{2}+2 v \omega_{5}-2 \omega_{2} v & -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5} & -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5} & 0 & -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5}\\ + -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6} & -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6} & -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6} & -1-2 w \omega_{3}+\omega_{3}+2 w \omega_{6} & -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6} & -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m5_matB_per_els.tex b/tex/d3q7/d3q7m5_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..8b4b94f2b10c592754f1f0ae0f7e25e4c21e60e7 --- /dev/null +++ b/tex/d3q7/d3q7m5_matB_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+2 \omega_{1} u+\omega_{4}-2 \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1-2 v \omega_{5}+2 \omega_{2} v+\omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{6}+2 w \omega_{3}-2 w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1-2 \omega_{1} u+\omega_{4}+2 \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,6} = -1+2 v \omega_{5}-2 \omega_{2} v+\omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,7} = -1+\omega_{6}-2 w \omega_{3}+2 w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+2 \omega_{1} u+\omega_{1}-2 \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,6} = -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,7} = -1+ \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}- \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,6} = -1+\omega_{2}-2 v \omega_{5}+2 \omega_{2} v, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,7} = -1+\frac{1}{2} \omega_{2}- v \omega_{5}+ \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,6} = -1+\frac{1}{2} \omega_{6}+ w \omega_{3}+\frac{1}{2} \omega_{3}- w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,7} = -1+2 w \omega_{3}+\omega_{3}-2 w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1-2 \omega_{1} u+\omega_{1}+2 \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,6} = -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,7} = -1- \omega_{1} u+\frac{1}{2} \omega_{4}+\frac{1}{2} \omega_{1}+ \omega_{4} u, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,1} = -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,2} = -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,3} = -1+\omega_{2}+2 v \omega_{5}-2 \omega_{2} v, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,4} = -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,5} = -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,7} = -1+\frac{1}{2} \omega_{2}+ v \omega_{5}- \omega_{2} v+\frac{1}{2} \omega_{5}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,1} = -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,2} = -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,3} = -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,4} = -1-2 w \omega_{3}+\omega_{3}+2 w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,5} = -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,6} = -1+\frac{1}{2} \omega_{6}- w \omega_{3}+\frac{1}{2} \omega_{3}+ w \omega_{6}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,7} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m5_matK.tex b/tex/d3q7/d3q7m5_matK.tex new file mode 100644 index 0000000000000000000000000000000000000000..17d827cf385361a5d81a609b447826be153380b3 --- /dev/null +++ b/tex/d3q7/d3q7m5_matK.tex @@ -0,0 +1,12 @@ +\noindent +\begin{equation*} +\matr{K} = \begin{pmatrix} + 1 &1 &1 &1 &1 &1 &1\\ + -u &1-u &-u &-u &-u-1 &-u &-u\\ + -v &-v &1-v &-v &-v &-v-1 &-v\\ + -w &-w &-w &1-w &-w &-w &-w-1\\ + u^2 &(1-u)^2 &u^2 &u^2 &(u+1)^2 &u^2 &u^2\\ + v^2 &v^2 &(1-v)^2 &v^2 &v^2 &(v+1)^2 &v^2\\ + w^2 &w^2 &w^2 &(1-w)^2 &w^2 &w^2 &(w+1)^2 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m5_matK_per_els.tex b/tex/d3q7/d3q7m5_matK_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..43636bb90ae20993695b5bad64995dfda4032254 --- /dev/null +++ b/tex/d3q7/d3q7m5_matK_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{K}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,1} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,2} = 1-u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,3} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,4} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,5} = (-u)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,6} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,7} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,1} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,2} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,3} = 1-v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,4} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,5} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,6} = (-v)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,7} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,1} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,2} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,3} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,4} = 1-w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,5} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,6} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,7} = (-w)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,1} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,2} = (1-u)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,3} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,4} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,5} = ((-u)-1)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,6} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,7} = u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,1} = v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,2} = v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,3} = (1-v)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,4} = v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,5} = v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,6} = ((-v)-1)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,7} = v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,1} = w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,2} = w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,3} = w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,4} = (1-w)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,5} = w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,6} = w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,7} = ((-w)-1)^2. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m5_matM.tex b/tex/d3q7/d3q7m5_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..e0e2f8f78d1855069a9fd41a74295b8f9fd4ad74 --- /dev/null +++ b/tex/d3q7/d3q7m5_matM.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 & 1 & 1 & 1 & 1 & 1 & 1\\ + 0 & 1 & 0 & 0 & -1 & 0 & 0\\ + 0 & 0 & 1 & 0 & 0 & -1 & 0\\ + 0 & 0 & 0 & 1 & 0 & 0 & -1\\ + 0 & 1 & 0 & 0 & 1 & 0 & 0\\ + 0 & 0 & 1 & 0 & 0 & 1 & 0\\ + 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m5_matM_per_els.tex b/tex/d3q7/d3q7m5_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..430493e1091e7a4211450c168ebcbd629795f35b --- /dev/null +++ b/tex/d3q7/d3q7m5_matM_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,7} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,7} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m6_feq.tex b/tex/d3q7/d3q7m6_feq.tex new file mode 100644 index 0000000000000000000000000000000000000000..ff82b62139939cf2bfa3945dc3d509552b93428c --- /dev/null +++ b/tex/d3q7/d3q7m6_feq.tex @@ -0,0 +1,13 @@ +Equilibrium DF vector $\vec{f}^{eq}$: +\noindent +\begin{equation*} +\vec{f}^{eq} = \begin{pmatrix} + 1-v^{2}-w^{2}-3 c_s^{2}-u^{2}\\ + \frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + \frac{1}{2} v+\frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} w^{2}+\frac{1}{2} w+\frac{1}{2} c_s^{2}\\ + -\frac{1}{2} u+\frac{1}{2} c_s^{2}+\frac{1}{2} u^{2}\\ + -\frac{1}{2} v+\frac{1}{2} v^{2}+\frac{1}{2} c_s^{2}\\ + \frac{1}{2} w^{2}-\frac{1}{2} w+\frac{1}{2} c_s^{2} +\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m6_matA.tex b/tex/d3q7/d3q7m6_matA.tex new file mode 100644 index 0000000000000000000000000000000000000000..dc75d98830efe382b54fb05624265cd98423d0a5 --- /dev/null +++ b/tex/d3q7/d3q7m6_matA.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{A} = \begin{pmatrix} + 2 v^{2} \omega_{2}+2 \omega_{1} u^{2}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}- \omega_{0} u^{2}- w^{2} \omega_{0} & -2 \omega_{1} u-\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}+2 \omega_{4} u- \omega_{0} u^{2}- w^{2} \omega_{0} & -\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}+2 v \omega_{4}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}-2 v \omega_{2}- \omega_{0} u^{2}- w^{2} \omega_{0} & 2 \omega_{4} w-\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}-2 w \omega_{3}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}- \omega_{0} u^{2}- w^{2} \omega_{0} & 2 \omega_{1} u-\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}-2 \omega_{4} u- \omega_{0} u^{2}- w^{2} \omega_{0} & -\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}-2 v \omega_{4}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}+2 v \omega_{2}- \omega_{0} u^{2}- w^{2} \omega_{0} & -2 \omega_{4} w-\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}+2 w \omega_{3}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}- \omega_{0} u^{2}- w^{2} \omega_{0}\\ + -\frac{1}{2} \omega_{1} u-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2} & \frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} \omega_{1}- \omega_{1} u^{2}-\frac{1}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}-\frac{1}{3} \omega_{6} u+\frac{1}{2} \omega_{0} u^{2} & -\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{6} \omega_{5}+\frac{1}{2} \omega_{0} u^{2} & -\frac{1}{3} \omega_{4} w-\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2} & -\frac{3}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} \omega_{1}- \omega_{1} u^{2}+\frac{1}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}+\frac{1}{3} \omega_{6} u+\frac{1}{2} \omega_{0} u^{2} & -\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{6} \omega_{5}+\frac{1}{2} \omega_{0} u^{2} & \frac{1}{3} \omega_{4} w-\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u-\frac{1}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2}\\ + - v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{2} v \omega_{2} & \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}+\frac{2}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{3} \omega_{4} u-\frac{1}{3} \omega_{5}-\frac{1}{2} v \omega_{2}-\frac{1}{3} \omega_{6} u & \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}-\frac{2}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{5}+\frac{1}{2} v \omega_{2}+\frac{1}{2} \omega_{2} & -\frac{1}{3} \omega_{4} w+\frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{3} w \omega_{6}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{2} v \omega_{2} & \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}-\frac{2}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{4} u-\frac{1}{3} \omega_{5}-\frac{1}{2} v \omega_{2}+\frac{1}{3} \omega_{6} u & \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{2}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{5}-\frac{3}{2} v \omega_{2}-\frac{1}{2} \omega_{2} & \frac{1}{3} \omega_{4} w+\frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{3} w \omega_{6}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{2} v \omega_{2}\\ + \frac{1}{2} w \omega_{0}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0} & \frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}-\frac{1}{3} u \omega_{5}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}+\frac{2}{3} \omega_{6} u+\frac{1}{2} w^{2} \omega_{0} & \frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{3} v \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{6} \omega_{5}+\frac{1}{2} w^{2} \omega_{0} & -\frac{1}{3} \omega_{4} w+\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{2} \omega_{3}-\frac{1}{3} \omega_{6} u^{2}-\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0} & \frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}+\frac{1}{3} u \omega_{5}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}-\frac{2}{3} \omega_{6} u+\frac{1}{2} w^{2} \omega_{0} & \frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} v \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{6} \omega_{5}+\frac{1}{2} w^{2} \omega_{0} & \frac{1}{3} \omega_{4} w+\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{3}{2} w \omega_{3}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{2} \omega_{3}-\frac{1}{3} \omega_{6} u^{2}+\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0}\\ + \frac{1}{2} \omega_{1} u-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2} & \frac{3}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} \omega_{1}- \omega_{1} u^{2}-\frac{1}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}-\frac{1}{3} \omega_{6} u+\frac{1}{2} \omega_{0} u^{2} & \frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{6} \omega_{5}+\frac{1}{2} \omega_{0} u^{2} & -\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2} & -\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} \omega_{1}- \omega_{1} u^{2}+\frac{1}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}+\frac{1}{3} \omega_{6} u+\frac{1}{2} \omega_{0} u^{2} & \frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{6} \omega_{5}+\frac{1}{2} \omega_{0} u^{2} & \frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u-\frac{1}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2}\\ + - v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} v \omega_{2} & \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}+\frac{2}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{3} \omega_{4} u-\frac{1}{3} \omega_{5}+\frac{1}{2} v \omega_{2}-\frac{1}{3} \omega_{6} u & \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}-\frac{2}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{5}+\frac{3}{2} v \omega_{2}-\frac{1}{2} \omega_{2} & -\frac{1}{3} \omega_{4} w+\frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{3} w \omega_{6}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} v \omega_{2} & \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}-\frac{2}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{4} u-\frac{1}{3} \omega_{5}+\frac{1}{2} v \omega_{2}+\frac{1}{3} \omega_{6} u & \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{2}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{5}-\frac{1}{2} v \omega_{2}+\frac{1}{2} \omega_{2} & \frac{1}{3} \omega_{4} w+\frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{3} w \omega_{6}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} v \omega_{2}\\ + -\frac{1}{2} w \omega_{0}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0} & -\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}-\frac{1}{3} u \omega_{5}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}+\frac{2}{3} \omega_{6} u+\frac{1}{2} w^{2} \omega_{0} & -\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{3} v \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{6} \omega_{5}+\frac{1}{2} w^{2} \omega_{0} & -\frac{1}{3} \omega_{4} w-\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{3}{2} w \omega_{3}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{2} \omega_{3}-\frac{1}{3} \omega_{6} u^{2}-\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0} & -\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}+\frac{1}{3} u \omega_{5}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}-\frac{2}{3} \omega_{6} u+\frac{1}{2} w^{2} \omega_{0} & -\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} v \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{6} \omega_{5}+\frac{1}{2} w^{2} \omega_{0} & \frac{1}{3} \omega_{4} w-\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{2} \omega_{3}-\frac{1}{3} \omega_{6} u^{2}+\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0}\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m6_matA_per_els.tex b/tex/d3q7/d3q7m6_matA_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..2ee47d8598cc698677274cb6fbccd1805c08f0db --- /dev/null +++ b/tex/d3q7/d3q7m6_matA_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{A}_{1,1} = 2 v^{2} \omega_{2}+2 \omega_{1} u^{2}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}- \omega_{0} u^{2}- w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,2} = -2 \omega_{1} u-\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}+2 \omega_{4} u- \omega_{0} u^{2}- w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,3} = -\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}+2 v \omega_{4}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}-2 v \omega_{2}- \omega_{0} u^{2}- w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,4} = 2 \omega_{4} w-\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}-2 w \omega_{3}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}- \omega_{0} u^{2}- w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,5} = 2 \omega_{1} u-\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}-2 \omega_{4} u- \omega_{0} u^{2}- w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,6} = -\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}-2 v \omega_{4}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}+2 v \omega_{2}- \omega_{0} u^{2}- w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{1,7} = -2 \omega_{4} w-\omega_{4}+2 v^{2} \omega_{2}+2 \omega_{1} u^{2}+2 w \omega_{3}- \omega_{4} w^{2}- v^{2} \omega_{4}- v^{2} \omega_{0}+\omega_{0}- \omega_{4} u^{2}+2 w^{2} \omega_{3}- \omega_{0} u^{2}- w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,1} = -\frac{1}{2} \omega_{1} u-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,2} = \frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} \omega_{1}- \omega_{1} u^{2}-\frac{1}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}-\frac{1}{3} \omega_{6} u+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,3} = -\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{6} \omega_{5}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,4} = -\frac{1}{3} \omega_{4} w-\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,5} = -\frac{3}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} \omega_{1}- \omega_{1} u^{2}+\frac{1}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}+\frac{1}{3} \omega_{6} u+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,6} = -\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{6} \omega_{5}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{2,7} = \frac{1}{3} \omega_{4} w-\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} \omega_{0} u-\frac{1}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,1} = - v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{2} v \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,2} = \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}+\frac{2}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{3} \omega_{4} u-\frac{1}{3} \omega_{5}-\frac{1}{2} v \omega_{2}-\frac{1}{3} \omega_{6} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,3} = \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}-\frac{2}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{5}+\frac{1}{2} v \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,4} = -\frac{1}{3} \omega_{4} w+\frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{3} w \omega_{6}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{2} v \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,5} = \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}-\frac{2}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{4} u-\frac{1}{3} \omega_{5}-\frac{1}{2} v \omega_{2}+\frac{1}{3} \omega_{6} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,6} = \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{2}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{5}-\frac{3}{2} v \omega_{2}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{3,7} = \frac{1}{3} \omega_{4} w+\frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} v \omega_{0}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{3} w \omega_{6}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{2} v \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,1} = \frac{1}{2} w \omega_{0}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,2} = \frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}-\frac{1}{3} u \omega_{5}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}+\frac{2}{3} \omega_{6} u+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,3} = \frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{3} v \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{6} \omega_{5}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,4} = -\frac{1}{3} \omega_{4} w+\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{2} \omega_{3}-\frac{1}{3} \omega_{6} u^{2}-\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,5} = \frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}+\frac{1}{3} u \omega_{5}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}-\frac{2}{3} \omega_{6} u+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,6} = \frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} v \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{6} \omega_{5}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{4,7} = \frac{1}{3} \omega_{4} w+\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{3}{2} w \omega_{3}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{2} \omega_{3}-\frac{1}{3} \omega_{6} u^{2}+\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,1} = \frac{1}{2} \omega_{1} u-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,2} = \frac{3}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} \omega_{1}- \omega_{1} u^{2}-\frac{1}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}-\frac{1}{3} \omega_{6} u+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,3} = \frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{6} \omega_{5}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,4} = -\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,5} = -\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}+\frac{1}{2} \omega_{1}- \omega_{1} u^{2}+\frac{1}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}+\frac{1}{3} \omega_{6} u+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,6} = \frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{6} \omega_{5}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{5,7} = \frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{1} u+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}- \omega_{1} u^{2}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{2} \omega_{0} u-\frac{1}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} \omega_{0} u^{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,1} = - v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} v \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,2} = \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}+\frac{2}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}-\frac{1}{3} \omega_{4} u-\frac{1}{3} \omega_{5}+\frac{1}{2} v \omega_{2}-\frac{1}{3} \omega_{6} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,3} = \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}-\frac{2}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{5}+\frac{3}{2} v \omega_{2}-\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,4} = -\frac{1}{3} \omega_{4} w+\frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{3} w \omega_{6}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} v \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,5} = \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}-\frac{2}{3} u \omega_{5}+\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{4} u-\frac{1}{3} \omega_{5}+\frac{1}{2} v \omega_{2}+\frac{1}{3} \omega_{6} u, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,6} = \frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{2}{3} v \omega_{5}+\frac{1}{6} \omega_{6} u^{2}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{3} \omega_{5}-\frac{1}{2} v \omega_{2}+\frac{1}{2} \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{6,7} = \frac{1}{3} \omega_{4} w+\frac{1}{6} \omega_{4}- v^{2} \omega_{2}+\frac{1}{3} v^{2} \omega_{5}-\frac{1}{6} w^{2} \omega_{6}-\frac{1}{2} v \omega_{0}-\frac{1}{6} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}-\frac{1}{3} u^{2} \omega_{5}+\frac{1}{6} \omega_{6} u^{2}-\frac{1}{3} w \omega_{6}+\frac{1}{2} v^{2} \omega_{0}+\frac{1}{6} \omega_{4} u^{2}+\frac{1}{2} v \omega_{2}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,1} = -\frac{1}{2} w \omega_{0}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,2} = -\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}-\frac{1}{3} u \omega_{5}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}+\frac{2}{3} \omega_{6} u+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,3} = -\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}-\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{3} v \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{6} \omega_{5}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,4} = -\frac{1}{3} \omega_{4} w-\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{3}{2} w \omega_{3}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{2} \omega_{3}-\frac{1}{3} \omega_{6} u^{2}-\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,5} = -\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}+\frac{1}{3} u \omega_{5}-\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{3} \omega_{4} u+\frac{1}{6} \omega_{5}-\frac{2}{3} \omega_{6} u+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,6} = -\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}+\frac{1}{2} w \omega_{3}+\frac{1}{3} v \omega_{4}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}-\frac{1}{3} v \omega_{5}-\frac{1}{3} \omega_{6} u^{2}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}-\frac{1}{6} \omega_{5}+\frac{1}{2} w^{2} \omega_{0}, + \end{dmath*} + \begin{dmath*} + \matr{A}_{7,7} = \frac{1}{3} \omega_{4} w-\frac{1}{2} w \omega_{0}+\frac{1}{6} \omega_{4}-\frac{1}{6} v^{2} \omega_{5}+\frac{1}{3} w^{2} \omega_{6}-\frac{1}{2} w \omega_{3}+\frac{1}{3} \omega_{6}+\frac{1}{6} \omega_{4} w^{2}+\frac{1}{6} v^{2} \omega_{4}+\frac{1}{6} u^{2} \omega_{5}+\frac{1}{2} \omega_{3}-\frac{1}{3} \omega_{6} u^{2}+\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4} u^{2}- w^{2} \omega_{3}+\frac{1}{2} w^{2} \omega_{0}. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m6_matB.tex b/tex/d3q7/d3q7m6_matB.tex new file mode 100644 index 0000000000000000000000000000000000000000..c7815b9bb6f687e15212dc50ba65ac8e1d9ff62b --- /dev/null +++ b/tex/d3q7/d3q7m6_matB.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{B} = \begin{pmatrix} + 0 & -1+2 u \omega_{1}+\omega_{4}-2 u \omega_{4} & -1+\omega_{4}+2 \omega_{2} v-2 v \omega_{4} & -1+\omega_{4}-2 \omega_{4} w+2 w \omega_{3} & -1-2 u \omega_{1}+\omega_{4}+2 u \omega_{4} & -1+\omega_{4}-2 \omega_{2} v+2 v \omega_{4} & -1+\omega_{4}+2 \omega_{4} w-2 w \omega_{3}\\ + -1+\frac{1}{6} \omega_{5}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4} & 0 & -1+\frac{1}{3} \omega_{5}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}-\frac{1}{3} \omega_{5} v+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}+\frac{1}{3} v \omega_{4} & -1+\frac{1}{6} \omega_{5}-\frac{1}{3} w \omega_{6}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w-\frac{1}{3} u \omega_{4} & -1+2 u \omega_{1}-\frac{2}{3} u \omega_{5}-\frac{2}{3} u \omega_{6}+\omega_{1}-\frac{2}{3} u \omega_{4} & -1+\frac{1}{3} \omega_{5}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}+\frac{1}{3} \omega_{5} v+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}-\frac{1}{3} v \omega_{4} & -1+\frac{1}{6} \omega_{5}+\frac{1}{3} w \omega_{6}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w-\frac{1}{3} u \omega_{4}\\ + -1+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+ \omega_{2} v-\frac{2}{3} \omega_{5} v-\frac{1}{3} v \omega_{4} & -1+\frac{2}{3} \omega_{5}-\frac{2}{3} u \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{3} u \omega_{6}+ \omega_{2} v-\frac{2}{3} \omega_{5} v-\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}-\frac{1}{3} v \omega_{4} & 0 & -1+\frac{1}{3} \omega_{5}-\frac{1}{3} w \omega_{6}+\frac{1}{2} \omega_{2}+ \omega_{2} v-\frac{2}{3} \omega_{5} v+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{4} w-\frac{1}{3} v \omega_{4} & -1+\frac{2}{3} \omega_{5}+\frac{2}{3} u \omega_{5}+\frac{1}{2} \omega_{2}-\frac{1}{3} u \omega_{6}+ \omega_{2} v-\frac{2}{3} \omega_{5} v-\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}-\frac{1}{3} v \omega_{4} & -1+\omega_{2}+2 \omega_{2} v-\frac{4}{3} \omega_{5} v-\frac{2}{3} v \omega_{4} & -1+\frac{1}{3} \omega_{5}+\frac{1}{3} w \omega_{6}+\frac{1}{2} \omega_{2}+ \omega_{2} v-\frac{2}{3} \omega_{5} v+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{4} w-\frac{1}{3} v \omega_{4}\\ + -1-\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+ w \omega_{3} & -1-\frac{1}{6} \omega_{5}-\frac{2}{3} w \omega_{6}+\frac{1}{3} u \omega_{5}-\frac{2}{3} u \omega_{6}+\frac{2}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+\frac{1}{3} u \omega_{4}+ w \omega_{3} & -1+\frac{1}{6} \omega_{5}-\frac{2}{3} w \omega_{6}-\frac{1}{3} \omega_{5} v+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+\frac{1}{3} v \omega_{4}+ w \omega_{3} & 0 & -1-\frac{1}{6} \omega_{5}-\frac{2}{3} w \omega_{6}-\frac{1}{3} u \omega_{5}+\frac{2}{3} u \omega_{6}+\frac{2}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}-\frac{1}{3} u \omega_{4}+ w \omega_{3} & -1+\frac{1}{6} \omega_{5}-\frac{2}{3} w \omega_{6}+\frac{1}{3} \omega_{5} v+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}-\frac{1}{3} v \omega_{4}+ w \omega_{3} & -1-\frac{4}{3} w \omega_{6}-\frac{2}{3} \omega_{4} w+\omega_{3}+2 w \omega_{3}\\ + -1+\frac{1}{6} \omega_{5}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4} & -1-2 u \omega_{1}+\frac{2}{3} u \omega_{5}+\frac{2}{3} u \omega_{6}+\omega_{1}+\frac{2}{3} u \omega_{4} & -1+\frac{1}{3} \omega_{5}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}-\frac{1}{3} \omega_{5} v+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}+\frac{1}{3} v \omega_{4} & -1+\frac{1}{6} \omega_{5}-\frac{1}{3} w \omega_{6}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{3} u \omega_{4} & 0 & -1+\frac{1}{3} \omega_{5}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}+\frac{1}{3} \omega_{5} v+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}-\frac{1}{3} v \omega_{4} & -1+\frac{1}{6} \omega_{5}+\frac{1}{3} w \omega_{6}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{3} u \omega_{4}\\ + -1+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}- \omega_{2} v+\frac{2}{3} \omega_{5} v+\frac{1}{3} v \omega_{4} & -1+\frac{2}{3} \omega_{5}-\frac{2}{3} u \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{3} u \omega_{6}- \omega_{2} v+\frac{2}{3} \omega_{5} v-\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}+\frac{1}{3} v \omega_{4} & -1+\omega_{2}-2 \omega_{2} v+\frac{4}{3} \omega_{5} v+\frac{2}{3} v \omega_{4} & -1+\frac{1}{3} \omega_{5}-\frac{1}{3} w \omega_{6}+\frac{1}{2} \omega_{2}- \omega_{2} v+\frac{2}{3} \omega_{5} v+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{3} v \omega_{4} & -1+\frac{2}{3} \omega_{5}+\frac{2}{3} u \omega_{5}+\frac{1}{2} \omega_{2}-\frac{1}{3} u \omega_{6}- \omega_{2} v+\frac{2}{3} \omega_{5} v-\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}+\frac{1}{3} v \omega_{4} & 0 & -1+\frac{1}{3} \omega_{5}+\frac{1}{3} w \omega_{6}+\frac{1}{2} \omega_{2}- \omega_{2} v+\frac{2}{3} \omega_{5} v+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{3} v \omega_{4}\\ + -1+\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}- w \omega_{3} & -1-\frac{1}{6} \omega_{5}+\frac{2}{3} w \omega_{6}+\frac{1}{3} u \omega_{5}-\frac{2}{3} u \omega_{6}+\frac{2}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+\frac{1}{3} u \omega_{4}- w \omega_{3} & -1+\frac{1}{6} \omega_{5}+\frac{2}{3} w \omega_{6}-\frac{1}{3} \omega_{5} v+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+\frac{1}{3} v \omega_{4}- w \omega_{3} & -1+\frac{4}{3} w \omega_{6}+\frac{2}{3} \omega_{4} w+\omega_{3}-2 w \omega_{3} & -1-\frac{1}{6} \omega_{5}+\frac{2}{3} w \omega_{6}-\frac{1}{3} u \omega_{5}+\frac{2}{3} u \omega_{6}+\frac{2}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}-\frac{1}{3} u \omega_{4}- w \omega_{3} & -1+\frac{1}{6} \omega_{5}+\frac{2}{3} w \omega_{6}+\frac{1}{3} \omega_{5} v+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}-\frac{1}{3} v \omega_{4}- w \omega_{3} & 0\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m6_matB_per_els.tex b/tex/d3q7/d3q7m6_matB_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..e5cc1e653b367a70201e81ad934d443f88b1b091 --- /dev/null +++ b/tex/d3q7/d3q7m6_matB_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{B}_{1,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,2} = -1+2 u \omega_{1}+\omega_{4}-2 u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,3} = -1+\omega_{4}+2 \omega_{2} v-2 v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,4} = -1+\omega_{4}-2 \omega_{4} w+2 w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,5} = -1-2 u \omega_{1}+\omega_{4}+2 u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,6} = -1+\omega_{4}-2 \omega_{2} v+2 v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{1,7} = -1+\omega_{4}+2 \omega_{4} w-2 w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,1} = -1+\frac{1}{6} \omega_{5}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,3} = -1+\frac{1}{3} \omega_{5}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}-\frac{1}{3} \omega_{5} v+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}+\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,4} = -1+\frac{1}{6} \omega_{5}-\frac{1}{3} w \omega_{6}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w-\frac{1}{3} u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,5} = -1+2 u \omega_{1}-\frac{2}{3} u \omega_{5}-\frac{2}{3} u \omega_{6}+\omega_{1}-\frac{2}{3} u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,6} = -1+\frac{1}{3} \omega_{5}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}+\frac{1}{3} \omega_{5} v+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}-\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{2,7} = -1+\frac{1}{6} \omega_{5}+\frac{1}{3} w \omega_{6}+ u \omega_{1}-\frac{1}{3} u \omega_{5}-\frac{1}{3} u \omega_{6}+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w-\frac{1}{3} u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,1} = -1+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}+ \omega_{2} v-\frac{2}{3} \omega_{5} v-\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,2} = -1+\frac{2}{3} \omega_{5}-\frac{2}{3} u \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{3} u \omega_{6}+ \omega_{2} v-\frac{2}{3} \omega_{5} v-\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}-\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,4} = -1+\frac{1}{3} \omega_{5}-\frac{1}{3} w \omega_{6}+\frac{1}{2} \omega_{2}+ \omega_{2} v-\frac{2}{3} \omega_{5} v+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{4} w-\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,5} = -1+\frac{2}{3} \omega_{5}+\frac{2}{3} u \omega_{5}+\frac{1}{2} \omega_{2}-\frac{1}{3} u \omega_{6}+ \omega_{2} v-\frac{2}{3} \omega_{5} v-\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}-\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,6} = -1+\omega_{2}+2 \omega_{2} v-\frac{4}{3} \omega_{5} v-\frac{2}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{3,7} = -1+\frac{1}{3} \omega_{5}+\frac{1}{3} w \omega_{6}+\frac{1}{2} \omega_{2}+ \omega_{2} v-\frac{2}{3} \omega_{5} v+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{4} w-\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,1} = -1-\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+ w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,2} = -1-\frac{1}{6} \omega_{5}-\frac{2}{3} w \omega_{6}+\frac{1}{3} u \omega_{5}-\frac{2}{3} u \omega_{6}+\frac{2}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+\frac{1}{3} u \omega_{4}+ w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,3} = -1+\frac{1}{6} \omega_{5}-\frac{2}{3} w \omega_{6}-\frac{1}{3} \omega_{5} v+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+\frac{1}{3} v \omega_{4}+ w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,5} = -1-\frac{1}{6} \omega_{5}-\frac{2}{3} w \omega_{6}-\frac{1}{3} u \omega_{5}+\frac{2}{3} u \omega_{6}+\frac{2}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}-\frac{1}{3} u \omega_{4}+ w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,6} = -1+\frac{1}{6} \omega_{5}-\frac{2}{3} w \omega_{6}+\frac{1}{3} \omega_{5} v+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}-\frac{1}{3} v \omega_{4}+ w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{4,7} = -1-\frac{4}{3} w \omega_{6}-\frac{2}{3} \omega_{4} w+\omega_{3}+2 w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,1} = -1+\frac{1}{6} \omega_{5}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}+\frac{1}{6} \omega_{4}+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,2} = -1-2 u \omega_{1}+\frac{2}{3} u \omega_{5}+\frac{2}{3} u \omega_{6}+\omega_{1}+\frac{2}{3} u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,3} = -1+\frac{1}{3} \omega_{5}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}-\frac{1}{3} \omega_{5} v+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}+\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,4} = -1+\frac{1}{6} \omega_{5}-\frac{1}{3} w \omega_{6}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{3} u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,6} = -1+\frac{1}{3} \omega_{5}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}+\frac{1}{3} \omega_{5} v+\frac{1}{2} \omega_{1}+\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}-\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{5,7} = -1+\frac{1}{6} \omega_{5}+\frac{1}{3} w \omega_{6}- u \omega_{1}+\frac{1}{3} u \omega_{5}+\frac{1}{3} u \omega_{6}+\frac{1}{2} \omega_{1}+\frac{1}{3} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{3} u \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,1} = -1+\frac{1}{3} \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{6} \omega_{4}- \omega_{2} v+\frac{2}{3} \omega_{5} v+\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,2} = -1+\frac{2}{3} \omega_{5}-\frac{2}{3} u \omega_{5}+\frac{1}{2} \omega_{2}+\frac{1}{3} u \omega_{6}- \omega_{2} v+\frac{2}{3} \omega_{5} v-\frac{1}{6} \omega_{6}+\frac{1}{3} u \omega_{4}+\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,3} = -1+\omega_{2}-2 \omega_{2} v+\frac{4}{3} \omega_{5} v+\frac{2}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,4} = -1+\frac{1}{3} \omega_{5}-\frac{1}{3} w \omega_{6}+\frac{1}{2} \omega_{2}- \omega_{2} v+\frac{2}{3} \omega_{5} v+\frac{1}{6} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,5} = -1+\frac{2}{3} \omega_{5}+\frac{2}{3} u \omega_{5}+\frac{1}{2} \omega_{2}-\frac{1}{3} u \omega_{6}- \omega_{2} v+\frac{2}{3} \omega_{5} v-\frac{1}{6} \omega_{6}-\frac{1}{3} u \omega_{4}+\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{B}_{6,7} = -1+\frac{1}{3} \omega_{5}+\frac{1}{3} w \omega_{6}+\frac{1}{2} \omega_{2}- \omega_{2} v+\frac{2}{3} \omega_{5} v+\frac{1}{6} \omega_{6}-\frac{1}{3} \omega_{4} w+\frac{1}{3} v \omega_{4}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,1} = -1+\frac{2}{3} w \omega_{6}+\frac{1}{6} \omega_{4}+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}- w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,2} = -1-\frac{1}{6} \omega_{5}+\frac{2}{3} w \omega_{6}+\frac{1}{3} u \omega_{5}-\frac{2}{3} u \omega_{6}+\frac{2}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+\frac{1}{3} u \omega_{4}- w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,3} = -1+\frac{1}{6} \omega_{5}+\frac{2}{3} w \omega_{6}-\frac{1}{3} \omega_{5} v+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}+\frac{1}{3} v \omega_{4}- w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,4} = -1+\frac{4}{3} w \omega_{6}+\frac{2}{3} \omega_{4} w+\omega_{3}-2 w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,5} = -1-\frac{1}{6} \omega_{5}+\frac{2}{3} w \omega_{6}-\frac{1}{3} u \omega_{5}+\frac{2}{3} u \omega_{6}+\frac{2}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}-\frac{1}{3} u \omega_{4}- w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,6} = -1+\frac{1}{6} \omega_{5}+\frac{2}{3} w \omega_{6}+\frac{1}{3} \omega_{5} v+\frac{1}{3} \omega_{6}+\frac{1}{3} \omega_{4} w+\frac{1}{2} \omega_{3}-\frac{1}{3} v \omega_{4}- w \omega_{3}, + \end{dmath*} + \begin{dmath*} + \matr{B}_{7,7} = 0. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/d3q7m6_matK.tex b/tex/d3q7/d3q7m6_matK.tex new file mode 100644 index 0000000000000000000000000000000000000000..61a831adec4e884bbffd5dfba9a3c6a4648cd9cb --- /dev/null +++ b/tex/d3q7/d3q7m6_matK.tex @@ -0,0 +1,12 @@ +\noindent +\begin{equation*} +\matr{K} = \begin{pmatrix} + 1 &1 &1 &1 &1 &1 &1\\ + -u &1-u &-u &-u &-u-1 &-u &-u\\ + -v &-v &1-v &-v &-v &-v-1 &-v\\ + -w &-w &-w &1-w &-w &-w &-w-1\\ + w^2+v^2+u^2 &w^2+v^2+(1-u)^2 &w^2+(1-v)^2+u^2 &(1-w)^2+v^2+u^2 &w^2+v^2+(u+1)^2 &w^2+(v+1)^2+u^2 &(w+1)^2+v^2+u^2\\ + u^2-v^2 &(1-u)^2-v^2 &u^2-(1-v)^2 &u^2-v^2 &(u+1)^2-v^2 &u^2-(v+1)^2 &u^2-v^2\\ + u^2-w^2 &(1-u)^2-w^2 &u^2-w^2 &u^2-(1-w)^2 &(u+1)^2-w^2 &u^2-w^2 &u^2-(w+1)^2 +\end{pmatrix} +\end{equation*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m6_matK_per_els.tex b/tex/d3q7/d3q7m6_matK_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..c47fb8421a3d86594e298a5a4954d3f9a6903b11 --- /dev/null +++ b/tex/d3q7/d3q7m6_matK_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{K}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,1} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,2} = 1-u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,3} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,4} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,5} = (-u)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,6} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{2,7} = -u, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,1} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,2} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,3} = 1-v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,4} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,5} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,6} = (-v)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{3,7} = -v, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,1} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,2} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,3} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,4} = 1-w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,5} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,6} = -w, + \end{dmath*} + \begin{dmath*} + \matr{K}_{4,7} = (-w)-1, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,1} = w^2+v^2+u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,2} = w^2+v^2+(1-u)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,3} = w^2+(1-v)^2+u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,4} = (1-w)^2+v^2+u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,5} = w^2+v^2+((-u)-1)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,6} = w^2+((-v)-1)^2+u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{5,7} = ((-w)-1)^2+v^2+u^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,1} = u^2-v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,2} = (1-u)^2-v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,3} = u^2-(1-v)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,4} = u^2-v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,5} = ((-u)-1)^2-v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,6} = u^2-((-v)-1)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{6,7} = u^2-v^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,1} = u^2-w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,2} = (1-u)^2-w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,3} = u^2-w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,4} = u^2-(1-w)^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,5} = ((-u)-1)^2-w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,6} = u^2-w^2, + \end{dmath*} + \begin{dmath*} + \matr{K}_{7,7} = u^2-((-w)-1)^2. + \end{dmath*} +\end{dgroup*} \ No newline at end of file diff --git a/tex/d3q7/d3q7m6_matM.tex b/tex/d3q7/d3q7m6_matM.tex new file mode 100644 index 0000000000000000000000000000000000000000..e0e2f8f78d1855069a9fd41a74295b8f9fd4ad74 --- /dev/null +++ b/tex/d3q7/d3q7m6_matM.tex @@ -0,0 +1,11 @@ +\noindent +\begin{equation*} +\matr{M} = \begin{pmatrix} + 1 & 1 & 1 & 1 & 1 & 1 & 1\\ + 0 & 1 & 0 & 0 & -1 & 0 & 0\\ + 0 & 0 & 1 & 0 & 0 & -1 & 0\\ + 0 & 0 & 0 & 1 & 0 & 0 & -1\\ + 0 & 1 & 0 & 0 & 1 & 0 & 0\\ + 0 & 0 & 1 & 0 & 0 & 1 & 0\\ + 0 & 0 & 0 & 1 & 0 & 0 & 1\end{pmatrix}. +\end{equation*} diff --git a/tex/d3q7/d3q7m6_matM_per_els.tex b/tex/d3q7/d3q7m6_matM_per_els.tex new file mode 100644 index 0000000000000000000000000000000000000000..430493e1091e7a4211450c168ebcbd629795f35b --- /dev/null +++ b/tex/d3q7/d3q7m6_matM_per_els.tex @@ -0,0 +1,150 @@ +\noindent +\begin{dgroup*} + \begin{dmath*} + \matr{M}_{1,1} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{1,7} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,5} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{2,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,6} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{3,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{4,7} = -1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,2} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,5} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{5,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,3} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,4} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,6} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{6,7} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,1} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,2} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,3} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,4} = 1, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,5} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,6} = 0, + \end{dmath*} + \begin{dmath*} + \matr{M}_{7,7} = 1. + \end{dmath*} +\end{dgroup*} diff --git a/tex/d3q7/supp_d3q7_defs.tex b/tex/d3q7/supp_d3q7_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..1bc1e1a0ec809bd564d785d3a9f89d3f02c050bf --- /dev/null +++ b/tex/d3q7/supp_d3q7_defs.tex @@ -0,0 +1,21 @@ +\section{Global definitions} +In $\mathbb{R}^3$, the position and velocity vectors are given by $\vx=(x,y,z)$ and $\vu=(u,v,w)$, respectively. +% Let +% \begin{align*} +% \phi_{k_1k_2}^\ell &:= \phi_{x+k_1\dl,y+k_2\dl}^{t+\ell\dt}=\phi(t-\ell\dt,(x+k_1\dl,y+k_2\dl)), +% \\ +% \left[ \psi \right]_{k_1k_2}^\ell &:= \psi(t-\ell\dt,(x+k_1\dl,y+k_2\dl)). +% \end{align*} +% Additionally, negative subscript numbers are denoted by $\bar n:=-n$, i.e., $\bar1:=-1$, $\bar2:=-2$, etc. +\noindent +\input{d3q7/d3q7_C} +\input{d3q7/d3q7m0_feq} +Lattice speed of sound: $c_s = \frac1{\sqrt{3}}$. + +\noindent +Moments $\vec{\mu} = \left( \mu_1, \mu_2, \dots, \mu_7 \right)^T$ are given by +$$ + \vec{\mu} = \matr{\hatM} \vec{f}, +$$ +where $\vec{f} = \left( f_1,f_2,\dots,f_7 \right)^T$ and +\input{d3q7/d3q7_matM} diff --git a/tex/d3q7/supp_d3q7m0_defs.tex b/tex/d3q7/supp_d3q7m0_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..e4b525ffe25823e4619d52f09ba40e1467832fc1 --- /dev/null +++ b/tex/d3q7/supp_d3q7m0_defs.tex @@ -0,0 +1,11 @@ +\subsection{Definitions} +Matrix $\matr{A}=\matr{S}$: +\input{d3q7/d3q7m0_matA} +where +$$ + \matr{S} = \mathrm{diag}(\omega,\omega,\omega,\omega,\omega,\omega,\omega). +$$ + +\noindent +Matrix $\matr{B}$: +\input{d3q7/d3q7m0_matB} diff --git a/tex/d3q7/supp_d3q7m1_defs.tex b/tex/d3q7/supp_d3q7m1_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..7cffa184885ae4203f887a81883a4cc9f0499620 --- /dev/null +++ b/tex/d3q7/supp_d3q7m1_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d3q7/d3q7m1_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4,\omega_5,\omega_6) +$$ +and +\input{d3q7/d3q7m1_matM} + +\noindent +Matrix $\matr{B}$: +\input{d3q7/d3q7m1_matB_per_els} diff --git a/tex/d3q7/supp_d3q7m2_defs.tex b/tex/d3q7/supp_d3q7m2_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..b2b9a77aea2ffb9eb607d7567a3d8288aebb0ba4 --- /dev/null +++ b/tex/d3q7/supp_d3q7m2_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d3q7/d3q7m2_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4,\omega_5,\omega_6) +$$ +and +\input{d3q7/d3q7m2_matM} + +\noindent +Matrix $\matr{B}$: +\input{d3q7/d3q7m2_matB_per_els} diff --git a/tex/d3q7/supp_d3q7m3_defs.tex b/tex/d3q7/supp_d3q7m3_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..8824897188bbe592ed8743ba4365d9e3f86579c4 --- /dev/null +++ b/tex/d3q7/supp_d3q7m3_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d3q7/d3q7m3_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4,\omega_5,\omega_6) +$$ +and +\input{d3q7/d3q7m3_matM} + +\noindent +Matrix $\matr{B}$: +\input{d3q7/d3q7m3_matB_per_els} diff --git a/tex/d3q7/supp_d3q7m4_defs.tex b/tex/d3q7/supp_d3q7m4_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..2bcefafd2e988a461136932a48f389b470960379 --- /dev/null +++ b/tex/d3q7/supp_d3q7m4_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{M}^{-1} \matr{S} \matr{M}$: +\input{d3q7/d3q7m4_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4,\omega_5,\omega_6) +$$ +and +\input{d3q7/d3q7m4_matM} + +\noindent +Matrix $\matr{B}$: +\input{d3q7/d3q7m4_matB_per_els} diff --git a/tex/d3q7/supp_d3q7m5_defs.tex b/tex/d3q7/supp_d3q7m5_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..1c29e0cccdf2527258eeb8a78cf75460d9bece94 --- /dev/null +++ b/tex/d3q7/supp_d3q7m5_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{K}^{-1} \matr{S} \matr{K}$: +\input{d3q7/d3q7m5_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4,\omega_5,\omega_6) +$$ +and +\input{d3q7/d3q7m5_matK} + +\noindent +Matrix $\matr{B}$: +\input{d3q7/d3q7m5_matB_per_els} diff --git a/tex/d3q7/supp_d3q7m6_defs.tex b/tex/d3q7/supp_d3q7m6_defs.tex new file mode 100644 index 0000000000000000000000000000000000000000..f513e1263137d6a2a912c09628fc1c58c602cf7f --- /dev/null +++ b/tex/d3q7/supp_d3q7m6_defs.tex @@ -0,0 +1,13 @@ +\subsection{Definitions} +Matrix $\matr{A} = \matr{K}^{-1} \matr{S} \matr{K}$: +\input{d3q7/d3q7m6_matA_per_els} +where +$$ + \matr{S} = \mathrm{diag}(\omega_0,\omega_1,\omega_2,\omega_3,\omega_4,\omega_5,\omega_6) +$$ +and +\input{d3q7/d3q7m6_matK_per_els} + +\noindent +Matrix $\matr{B}$: +\input{d3q7/d3q7m6_matB_per_els} diff --git a/tex/header.tex b/tex/header.tex new file mode 100644 index 0000000000000000000000000000000000000000..c1532936c77a02bef6d55550d78a34f630e9fb5d --- /dev/null +++ b/tex/header.tex @@ -0,0 +1,120 @@ +%\documentclass[10pt]{elsarticle} +\documentclass[10pt]{article} + +\usepackage{authblk} +\usepackage[utf8]{inputenc} +\usepackage{amsmath} +\usepackage{amsthm} +\usepackage{amssymb} +\usepackage{graphicx} +\usepackage{color} +\usepackage{bm} +\usepackage{lineno,hyperref} +\usepackage[colorinlistoftodos,prependcaption,textsize=tiny]{todonotes} +\usepackage{subcaption} +\usepackage{algorithm} +\usepackage[left=2cm,right=2cm,a4paper]{geometry} + +\usepackage{breqn} % break equations automatically +%\breqnsetup{breakdepth={1},compact} +\usepackage{framed} +\usepackage{setspace} +\usepackage{longtable} +\usepackage{booktabs} +\let\vec\boldsymbol + +\newcommand{\matr}[1]{\mathbf{#1}} % undergraduate algebra version +\newcommand{\va}{{\vec{\alpha}}} +\newcommand{\vy}{{\vec{y}}} +\newcommand{\vx}{{\vec{x}}} +\newcommand{\vz}{{\vec{z}}} +\newcommand{\vc}{{\vec{c}}} +\newcommand{\vb}{{\vec{b}}} +\newcommand{\vp}{{\vec{p}}} +\newcommand{\vq}{{\vec{q}}} +\newcommand{\vu}{{\vec{u}}} +\newcommand{\dt}{{\delta_t}} +\newcommand{\dl}{{\delta_l}} +\newcommand{\norm}[1]{\left| #1\right|} +\newcommand{\ud}{\mathrm{d}} + +\usepackage[np]{numprint} +\npstyleenglish +\npproductsign{\cdot} +\npthousandsep{} % eliminate thousand separator to the left of the decimal point +\npthousandthpartsep{} % eliminate thousand separator to the right of the decimal point + +\newcount\colveccount +\newcommand*\colvec[1]{ + \global\colveccount#1 + \begin{pmatrix} + \colvecnext + } + \def\colvecnext#1{ + #1 + \global\advance\colveccount-1 + \ifnum\colveccount>0 + \\ + \expandafter\colvecnext + \else + \end{pmatrix} + \fi +} + +\setcounter{MaxMatrixCols}{30} + +%\usepackage{multicol} +% packages for EOC tables etc. +%\usepackage{booktabs} +%\usepackage{multirow} +%\newcommand{\shiftleft}[2]{\makebox[0pt][r]{\makebox[#1][l]{#2}}} +%\newcommand{\shiftright}[2]{\makebox[#1][r]{\makebox[0pt][l]{#2}}} + +\bibliographystyle{elsarticle-num} + +\newcommand{\titler}[3] +{ + \title{ + \textbf{#1 for #2 with #3}, + \\ + {supplementary material for} + \\ + \textbf{ + Equivalent Finite Difference Equations and Equivalent Partial Differential Equations for the Lattice Boltzmann Method + } + } + \date{} + \author[$\dagger$]{Radek Fu\v{c}\'{\i}k} + \author[$\ddag$,$\dagger$]{Robert Straka} + \affil[$\dagger$]{Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic} + \affil[$\ddag$]{AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland} +} + +\newcommand{\mmA}{\mu_{1}} +\newcommand{\mmB}{\mu_{2}} +\newcommand{\mmC}{\mu_{3}} +\newcommand{\mmD}{\mu_{4}} +\newcommand{\mmE}{\mu_{5}} +\newcommand{\mmF}{\mu_{6}} +\newcommand{\mmG}{\mu_{7}} +\newcommand{\mmH}{\mu_{8}} +\newcommand{\mmI}{\mu_{9}} +\newcommand{\mmJ}{\mu_{10}} +\newcommand{\mmK}{\mu_{11}} +\newcommand{\mmL}{\mu_{12}} +\newcommand{\mmM}{\mu_{13}} +\newcommand{\mmN}{\mu_{14}} +\newcommand{\mmO}{\mu_{15}} +\newcommand{\mmP}{\mu_{16}} +\newcommand{\mmQ}{\mu_{17}} +\newcommand{\mmR}{\mu_{18}} +\newcommand{\mmS}{\mu_{19}} +\newcommand{\mmT}{\mu_{20}} +\newcommand{\mmU}{\mu_{21}} +\newcommand{\mmV}{\mu_{22}} +\newcommand{\mmW}{\mu_{23}} +\newcommand{\mmX}{\mu_{24}} +\newcommand{\mmY}{\mu_{25}} +\newcommand{\mmZ}{\mu_{26}} +\newcommand{\mmAA}{\mu_{27}} +\newcommand{\hatM}{\tilde M} \ No newline at end of file diff --git a/tex/supp_d1q3c_efde.pdf b/tex/supp_d1q3c_efde.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0e1aec4a5fcdde70f0a0e9dc08e29d318ed6be7d Binary files /dev/null and b/tex/supp_d1q3c_efde.pdf differ diff --git a/tex/supp_d1q3c_efde.tex b/tex/supp_d1q3c_efde.tex new file mode 100644 index 0000000000000000000000000000000000000000..a8dd06c5345e2638434173ea68d5d8348689cdb0 --- /dev/null +++ b/tex/supp_d1q3c_efde.tex @@ -0,0 +1,33 @@ +\input{header} + +\titler{EFDE}{D1Q3}{constant velocities} + +\input{d1q3/d1q3_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d1q3/supp_d1q3_defs} + +\section{SRT} +\input{d1q3/supp_d1q3m0_defs} +\subsection{EFDE for $\mmA$}\input{../output_D1Q3c/d1q3m0c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D1Q3c/d1q3m0c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D1Q3c/d1q3m0c_efde2} + +\section{MRT} +\input{d1q3/supp_d1q3m1_defs} +\subsection{EFDE for $\mmA$}\input{../output_D1Q3c/d1q3m1c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D1Q3c/d1q3m1c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D1Q3c/d1q3m1c_efde2} + +\section{CLBM} +\input{d1q3/supp_d1q3m5_defs} +\subsection{EFDE for $\mmA$}\input{../output_D1Q3c/d1q3m5c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D1Q3c/d1q3m5c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D1Q3c/d1q3m5c_efde2} + + + +\end{document} diff --git a/tex/supp_d1q3c_epde.pdf b/tex/supp_d1q3c_epde.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c2c11a555e110d745c5a9798537d2acd1855c5f5 Binary files /dev/null and b/tex/supp_d1q3c_epde.pdf differ diff --git a/tex/supp_d1q3c_epde.tex b/tex/supp_d1q3c_epde.tex new file mode 100644 index 0000000000000000000000000000000000000000..15ca9344b84f4045bc6e26a7ab39a0ea22243463 --- /dev/null +++ b/tex/supp_d1q3c_epde.tex @@ -0,0 +1,31 @@ +\input{header} + +\titler{EPDE}{D1Q3}{constant velocities} + +\input{d1q3/d1q3_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d1q3/supp_d1q3_defs} + +\section{SRT} +\input{d1q3/supp_d1q3m0_defs} +\subsection{EPDE for $\mmA$}\input{../output_D1Q3c/d1q3m0c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D1Q3c/d1q3m0c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D1Q3c/d1q3m0c_epde2} + +\section{MRT} +\input{d1q3/supp_d1q3m1_defs} +\subsection{EPDE for $\mmA$}\input{../output_D1Q3c/d1q3m1c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D1Q3c/d1q3m1c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D1Q3c/d1q3m1c_epde2} + +\section{CLBM} +\input{d1q3/supp_d1q3m5_defs} +\subsection{EPDE for $\mmA$}\input{../output_D1Q3c/d1q3m5c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D1Q3c/d1q3m5c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D1Q3c/d1q3m5c_epde2} + +\end{document} diff --git a/tex/supp_d1q3n_efde.tex b/tex/supp_d1q3n_efde.tex new file mode 100644 index 0000000000000000000000000000000000000000..1a18a3a794911c58a635e067d84e044128b5f3c2 --- /dev/null +++ b/tex/supp_d1q3n_efde.tex @@ -0,0 +1,44 @@ +\input{header} + +\titler{EFDE}{D1Q3}{variable velocities} + +\input{d1q3/d1q3_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d1q3/supp_d1q3_defs} +\noindent +The following simplified notation is used: +\begin{align*} + u_{\ell,k} &:= u_{x+k\dl}^{t+\ell\dt} = u(t-\ell\dt,(x+k\dl)), +\end{align*} +with +\begin{align*} + u &:= u_{0,0}. +\end{align*} +Negative subscript numbers are denoted by $\bar n:=-n$, $\forall n\in\mathbb{N}$, i.e., $\bar1:=-1$, $\bar2:=-2$, etc. + + +\section{SRT} +\input{d1q3/supp_d1q3m0_defs} +\subsection{EFDE for $\mmA$}\input{../output_D1Q3n/d1q3m0n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D1Q3n/d1q3m0n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D1Q3n/d1q3m0n_efde2} + +\section{MRT} +\input{d1q3/supp_d1q3m1_defs} +\subsection{EFDE for $\mmA$}\input{../output_D1Q3n/d1q3m1n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D1Q3n/d1q3m1n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D1Q3n/d1q3m1n_efde2} + +\section{CLBM} +\input{d1q3/supp_d1q3m5_defs} +\subsection{EFDE for $\mmA$}\input{../output_D1Q3n/d1q3m5n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D1Q3n/d1q3m5n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D1Q3n/d1q3m5n_efde2} + + + +\end{document} diff --git a/tex/supp_d1q3n_epde.tex b/tex/supp_d1q3n_epde.tex new file mode 100644 index 0000000000000000000000000000000000000000..90dc84d7a5527b6d78e7a845b20550f7a38c8345 --- /dev/null +++ b/tex/supp_d1q3n_epde.tex @@ -0,0 +1,31 @@ +\input{header} + +\titler{EPDE}{D1Q3}{variable velocities} + +\input{d1q3/d1q3_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d1q3/supp_d1q3_defs} + +\section{SRT} +\input{d1q3/supp_d1q3m0_defs} +\subsection{EPDE for $\mmA$}\input{../output_D1Q3n/d1q3m0n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D1Q3n/d1q3m0n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D1Q3n/d1q3m0n_epde2} + +\section{MRT} +\input{d1q3/supp_d1q3m1_defs} +\subsection{EPDE for $\mmA$}\input{../output_D1Q3n/d1q3m1n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D1Q3n/d1q3m1n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D1Q3n/d1q3m1n_epde2} + +\section{CLBM} +\input{d1q3/supp_d1q3m5_defs} +\subsection{EPDE for $\mmA$}\input{../output_D1Q3n/d1q3m5n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D1Q3n/d1q3m5n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D1Q3n/d1q3m5n_epde2} + +\end{document} diff --git a/tex/supp_d2q5c_efde.pdf b/tex/supp_d2q5c_efde.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e64c61d0b13534d64872559c9a36ce2c6178051f Binary files /dev/null and b/tex/supp_d2q5c_efde.pdf differ diff --git a/tex/supp_d2q5c_efde.tex b/tex/supp_d2q5c_efde.tex new file mode 100644 index 0000000000000000000000000000000000000000..49b44db4f10e0277b4a57af2669293810806fcc0 --- /dev/null +++ b/tex/supp_d2q5c_efde.tex @@ -0,0 +1,69 @@ +\input{header} + +\titler{EFDE}{D2Q5}{constant velocities} + +\input{d2q5/d2q5_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d2q5/supp_d2q5_defs} + +\section{SRT} +\input{d2q5/supp_d2q5m0_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5c/d2q5m0c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5c/d2q5m0c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5c/d2q5m0c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5c/d2q5m0c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5c/d2q5m0c_efde4} + +\section{MRT 1: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$} +\input{d2q5/supp_d2q5m1_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5c/d2q5m1c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5c/d2q5m1c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5c/d2q5m1c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5c/d2q5m1c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5c/d2q5m1c_efde4} + +\section{MRT 2: relaxation of $\mA$, $\mB$, $\mC$, $\mD+\mE$, $\mD-\mE$} +\input{d2q5/supp_d2q5m2_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5c/d2q5m2c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5c/d2q5m2c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5c/d2q5m2c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5c/d2q5m2c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5c/d2q5m2c_efde4} + +\section{MRT 3: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$} +\input{d2q5/supp_d2q5m3_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5c/d2q5m3c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5c/d2q5m3c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5c/d2q5m3c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5c/d2q5m3c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5c/d2q5m3c_efde4} + +\section{MRT 4: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD+\mE$, $\mD-\mE$} +\input{d2q5/supp_d2q5m4_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5c/d2q5m4c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5c/d2q5m4c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5c/d2q5m4c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5c/d2q5m4c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5c/d2q5m4c_efde4} + +\section{CLBM 1: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE$} +\input{d2q5/supp_d2q5m5_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5c/d2q5m5c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5c/d2q5m5c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5c/d2q5m5c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5c/d2q5m5c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5c/d2q5m5c_efde4} + +\section{CLBM 2: relaxation of $\kA$, $\kB$, $\kC$, $\kD+\kE$, $\kD-\kE$} +\input{d2q5/supp_d2q5m6_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5c/d2q5m6c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5c/d2q5m6c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5c/d2q5m6c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5c/d2q5m6c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5c/d2q5m6c_efde4} + +\end{document} diff --git a/tex/supp_d2q5c_epde.pdf b/tex/supp_d2q5c_epde.pdf new file mode 100644 index 0000000000000000000000000000000000000000..56a942d2afbf9a1d6b0d050d82b6466dc3e21f38 Binary files /dev/null and b/tex/supp_d2q5c_epde.pdf differ diff --git a/tex/supp_d2q5c_epde.tex b/tex/supp_d2q5c_epde.tex new file mode 100644 index 0000000000000000000000000000000000000000..0bcf6c5487c419c022ae601b2e23d6670dfc302e --- /dev/null +++ b/tex/supp_d2q5c_epde.tex @@ -0,0 +1,69 @@ +\input{header} + +\titler{EPDE}{D2Q5}{constant velocities} + +\input{d2q5/d2q5_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d2q5/supp_d2q5_defs} + +\section{SRT} +\input{d2q5/supp_d2q5m0_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5c/d2q5m0c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5c/d2q5m0c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5c/d2q5m0c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5c/d2q5m0c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5c/d2q5m0c_epde4} + +\section{MRT 1: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$} +\input{d2q5/supp_d2q5m1_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5c/d2q5m1c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5c/d2q5m1c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5c/d2q5m1c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5c/d2q5m1c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5c/d2q5m1c_epde4} + +\section{MRT 2: relaxation of $\mA$, $\mB$, $\mC$, $\mD+\mE$, $\mD-\mE$} +\input{d2q5/supp_d2q5m2_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5c/d2q5m2c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5c/d2q5m2c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5c/d2q5m2c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5c/d2q5m2c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5c/d2q5m2c_epde4} + +\section{MRT 3: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$} +\input{d2q5/supp_d2q5m3_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5c/d2q5m3c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5c/d2q5m3c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5c/d2q5m3c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5c/d2q5m3c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5c/d2q5m3c_epde4} + +\section{MRT 4: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD+\mE$, $\mD-\mE$} +\input{d2q5/supp_d2q5m4_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5c/d2q5m4c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5c/d2q5m4c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5c/d2q5m4c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5c/d2q5m4c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5c/d2q5m4c_epde4} + +\section{CLBM 1: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE$} +\input{d2q5/supp_d2q5m5_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5c/d2q5m5c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5c/d2q5m5c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5c/d2q5m5c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5c/d2q5m5c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5c/d2q5m5c_epde4} + +\section{CLBM 2: relaxation of $\kA$, $\kB$, $\kC$, $\kD+\kE$, $\kD-\kE$} +\input{d2q5/supp_d2q5m6_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5c/d2q5m6c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5c/d2q5m6c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5c/d2q5m6c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5c/d2q5m6c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5c/d2q5m6c_epde4} + +\end{document} diff --git a/tex/supp_d2q5n_efde.tex b/tex/supp_d2q5n_efde.tex new file mode 100644 index 0000000000000000000000000000000000000000..0a63e2cb279439351d08dfa6989b682eb8cd47a7 --- /dev/null +++ b/tex/supp_d2q5n_efde.tex @@ -0,0 +1,85 @@ +\input{header} + +\titler{EFDE}{D2Q5}{variable velocities} + +\input{d2q5/d2q5_defs} + + + + +\begin{document} +\maketitle +\tableofcontents + +\input{d2q5/supp_d2q5_defs} + +\noindent +The following simplified notation is used: +\begin{align*} + u_{\ell,k_1k_2} &:= u_{x+k_1\dl,y+k_2\dl}^{t+\ell\dt} = u(t-\ell\dt,(x+k_1\dl,y+k_2\dl)), \\ + v_{\ell,k_1k_2} &:= v_{x+k_1\dl,y+k_2\dl}^{t+\ell\dt} = v(t-\ell\dt,(x+k_1\dl,y+k_2\dl)), +\end{align*} +with +\begin{align*} + u &:= u_{0,00}, \\ + v &:= v_{0,00}. +\end{align*} +Negative subscript numbers are denoted by $\bar n:=-n$, $\forall n\in\mathbb{N}$, i.e., $\bar1:=-1$, $\bar2:=-2$, etc. + +\section{SRT} +\input{d2q5/supp_d2q5m0_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5n/d2q5m0n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5n/d2q5m0n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5n/d2q5m0n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5n/d2q5m0n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5n/d2q5m0n_efde4} + +\section{MRT 1: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$} +\input{d2q5/supp_d2q5m1_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5n/d2q5m1n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5n/d2q5m1n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5n/d2q5m1n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5n/d2q5m1n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5n/d2q5m1n_efde4} + +\section{MRT 2: relaxation of $\mA$, $\mB$, $\mC$, $\mD+\mE$, $\mD-\mE$} +\input{d2q5/supp_d2q5m2_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5n/d2q5m2n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5n/d2q5m2n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5n/d2q5m2n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5n/d2q5m2n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5n/d2q5m2n_efde4} + +\section{MRT 3: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$} +\input{d2q5/supp_d2q5m3_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5n/d2q5m3n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5n/d2q5m3n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5n/d2q5m3n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5n/d2q5m3n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5n/d2q5m3n_efde4} + +\section{MRT 4: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD+\mE$, $\mD-\mE$} +\input{d2q5/supp_d2q5m4_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5n/d2q5m4n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5n/d2q5m4n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5n/d2q5m4n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5n/d2q5m4n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5n/d2q5m4n_efde4} + +\section{CLBM 1: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE$} +\input{d2q5/supp_d2q5m5_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5n/d2q5m5n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5n/d2q5m5n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5n/d2q5m5n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5n/d2q5m5n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5n/d2q5m5n_efde4} + +\section{CLBM 2: relaxation of $\kA$, $\kB$, $\kC$, $\kD+\kE$, $\kD-\kE$} +\input{d2q5/supp_d2q5m6_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D2Q5n/d2q5m6n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D2Q5n/d2q5m6n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D2Q5n/d2q5m6n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D2Q5n/d2q5m6n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D2Q5n/d2q5m6n_efde4} + +\end{document} diff --git a/tex/supp_d2q5n_epde.tex b/tex/supp_d2q5n_epde.tex new file mode 100644 index 0000000000000000000000000000000000000000..4f02bdfa42a4139d55617dc0303ffab238f400f2 --- /dev/null +++ b/tex/supp_d2q5n_epde.tex @@ -0,0 +1,72 @@ +\input{header} + +\titler{EPDE}{D2Q5}{variable velocities} + +\input{d2q5/d2q5_defs} + + + + +\begin{document} +\maketitle +\tableofcontents + +\input{d2q5/supp_d2q5_defs} + +\section{SRT} +\input{d2q5/supp_d2q5m0_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5n/d2q5m0n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5n/d2q5m0n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5n/d2q5m0n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5n/d2q5m0n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5n/d2q5m0n_epde4} + +\section{MRT 1: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$} +\input{d2q5/supp_d2q5m1_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5n/d2q5m1n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5n/d2q5m1n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5n/d2q5m1n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5n/d2q5m1n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5n/d2q5m1n_epde4} + +\section{MRT 2: relaxation of $\mA$, $\mB$, $\mC$, $\mD+\mE$, $\mD-\mE$} +\input{d2q5/supp_d2q5m2_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5n/d2q5m2n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5n/d2q5m2n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5n/d2q5m2n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5n/d2q5m2n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5n/d2q5m2n_epde4} + +\section{MRT 3: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$} +\input{d2q5/supp_d2q5m3_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5n/d2q5m3n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5n/d2q5m3n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5n/d2q5m3n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5n/d2q5m3n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5n/d2q5m3n_epde4} + +\section{MRT 4: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD+\mE$, $\mD-\mE$} +\input{d2q5/supp_d2q5m4_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5n/d2q5m4n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5n/d2q5m4n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5n/d2q5m4n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5n/d2q5m4n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5n/d2q5m4n_epde4} + +\section{CLBM 1: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE$} +\input{d2q5/supp_d2q5m5_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5n/d2q5m5n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5n/d2q5m5n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5n/d2q5m5n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5n/d2q5m5n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5n/d2q5m5n_epde4} + +\section{CLBM 2: relaxation of $\kA$, $\kB$, $\kC$, $\kD+\kE$, $\kD-\kE$} +\input{d2q5/supp_d2q5m6_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D2Q5n/d2q5m6n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D2Q5n/d2q5m6n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D2Q5n/d2q5m6n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D2Q5n/d2q5m6n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D2Q5n/d2q5m6n_epde4} + +\end{document} diff --git a/tex/supp_d3q7c_efde.tex b/tex/supp_d3q7c_efde.tex new file mode 100644 index 0000000000000000000000000000000000000000..00d67fe0c70a138ae21cc15d077d133f4f08205f --- /dev/null +++ b/tex/supp_d3q7c_efde.tex @@ -0,0 +1,84 @@ +\input{header} + +\titler{EFDE}{D3Q7}{constant velocities} + +\input{d3q7/d3q7_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d3q7/supp_d3q7_defs} + +\section{SRT} +\input{d3q7/supp_d3q7m0_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7c/d3q7m0c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7c/d3q7m0c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7c/d3q7m0c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7c/d3q7m0c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7c/d3q7m0c_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7c/d3q7m0c_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7c/d3q7m0c_efde6} + +\section{MRT 1: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$, $\mF$, $\mG$} +\input{d3q7/supp_d3q7m1_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7c/d3q7m1c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7c/d3q7m1c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7c/d3q7m1c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7c/d3q7m1c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7c/d3q7m1c_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7c/d3q7m1c_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7c/d3q7m1c_efde6} + +\section{MRT 2: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE+\mF+\mG$, $\mE-\mF$, $\mE-\mF$} +\input{d3q7/supp_d3q7m2_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7c/d3q7m2c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7c/d3q7m2c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7c/d3q7m2c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7c/d3q7m2c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7c/d3q7m2c_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7c/d3q7m2c_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7c/d3q7m2c_efde6} + +\section{MRT 3: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$, $\mF$, $\mG$} +\input{d3q7/supp_d3q7m3_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7c/d3q7m3c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7c/d3q7m3c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7c/d3q7m3c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7c/d3q7m3c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7c/d3q7m3c_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7c/d3q7m3c_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7c/d3q7m3c_efde6} + +\section{MRT 4: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE+\mF+\mG$, $\mE-\mF$, $\mE-\mF$} +\input{d3q7/supp_d3q7m4_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7c/d3q7m4c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7c/d3q7m4c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7c/d3q7m4c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7c/d3q7m4c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7c/d3q7m4c_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7c/d3q7m4c_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7c/d3q7m4c_efde6} + +\section{CLBM 1: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE$, $\kF$, $\kG$} +\input{d3q7/supp_d3q7m5_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7c/d3q7m5c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7c/d3q7m5c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7c/d3q7m5c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7c/d3q7m5c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7c/d3q7m5c_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7c/d3q7m5c_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7c/d3q7m5c_efde6} + +\section{CLBM 2: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE+\kF+\kG$, $\kE-\kF$, $\kE-\kG$} +\input{d3q7/supp_d3q7m6_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7c/d3q7m6c_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7c/d3q7m6c_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7c/d3q7m6c_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7c/d3q7m6c_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7c/d3q7m6c_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7c/d3q7m6c_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7c/d3q7m6c_efde6} + +\end{document} + diff --git a/tex/supp_d3q7c_epde.tex b/tex/supp_d3q7c_epde.tex new file mode 100644 index 0000000000000000000000000000000000000000..e4e3f7830b9820856124ca47a2352677cc391648 --- /dev/null +++ b/tex/supp_d3q7c_epde.tex @@ -0,0 +1,84 @@ +\input{header} + +\titler{EPDE}{D3Q7}{constant velocities} + +\input{d3q7/d3q7_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d3q7/supp_d3q7_defs} + +\section{SRT} +\input{d3q7/supp_d3q7m0_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7c/d3q7m0c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7c/d3q7m0c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7c/d3q7m0c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7c/d3q7m0c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7c/d3q7m0c_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7c/d3q7m0c_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7c/d3q7m0c_epde6} + +\section{MRT 1: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$, $\mF$, $\mG$} +\input{d3q7/supp_d3q7m1_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7c/d3q7m1c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7c/d3q7m1c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7c/d3q7m1c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7c/d3q7m1c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7c/d3q7m1c_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7c/d3q7m1c_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7c/d3q7m1c_epde6} + +\section{MRT 2: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE+\mF+\mG$, $\mE-\mF$, $\mE-\mF$} +\input{d3q7/supp_d3q7m2_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7c/d3q7m2c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7c/d3q7m2c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7c/d3q7m2c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7c/d3q7m2c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7c/d3q7m2c_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7c/d3q7m2c_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7c/d3q7m2c_epde6} + +\section{MRT 3: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$, $\mF$, $\mG$} +\input{d3q7/supp_d3q7m3_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7c/d3q7m3c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7c/d3q7m3c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7c/d3q7m3c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7c/d3q7m3c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7c/d3q7m3c_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7c/d3q7m3c_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7c/d3q7m3c_epde6} + +\section{MRT 4: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE+\mF+\mG$, $\mE-\mF$, $\mE-\mF$} +\input{d3q7/supp_d3q7m4_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7c/d3q7m4c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7c/d3q7m4c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7c/d3q7m4c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7c/d3q7m4c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7c/d3q7m4c_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7c/d3q7m4c_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7c/d3q7m4c_epde6} + +\section{CLBM 1: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE$, $\kF$, $\kG$} +\input{d3q7/supp_d3q7m5_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7c/d3q7m5c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7c/d3q7m5c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7c/d3q7m5c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7c/d3q7m5c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7c/d3q7m5c_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7c/d3q7m5c_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7c/d3q7m5c_epde6} + +\section{CLBM 2: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE+\kF+\kG$, $\kE-\kF$, $\kE-\kG$} +\input{d3q7/supp_d3q7m6_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7c/d3q7m6c_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7c/d3q7m6c_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7c/d3q7m6c_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7c/d3q7m6c_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7c/d3q7m6c_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7c/d3q7m6c_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7c/d3q7m6c_epde6} + +\end{document} + diff --git a/tex/supp_d3q7n_efde.tex b/tex/supp_d3q7n_efde.tex new file mode 100644 index 0000000000000000000000000000000000000000..205fcd09bad537e722db760949b149469a8df303 --- /dev/null +++ b/tex/supp_d3q7n_efde.tex @@ -0,0 +1,99 @@ +\input{header} + +\titler{EFDE}{D3Q7}{variable velocities} + +\input{d3q7/d3q7_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d3q7/supp_d3q7_defs} + +\noindent +The following simplified notation is used: +\begin{align*} + u_{\ell,k_1k_2k_3} &:= u_{x+k_1\dl,y+k_2\dl,z+k_3\dl}^{t+\ell\dt} = u(t-\ell\dt,(x+k_1\dl,y+k_2\dl,z+k_3\dl)), \\ + v_{\ell,k_1k_2k_3} &:= v_{x+k_1\dl,y+k_2\dl,z+k_3\dl}^{t+\ell\dt} = v(t-\ell\dt,(x+k_1\dl,y+k_2\dl,z+k_3\dl)), \\ + w_{\ell,k_1k_2k_3} &:= w_{x+k_1\dl,y+k_2\dl,z+k_3\dl}^{t+\ell\dt} = w(t-\ell\dt,(x+k_1\dl,y+k_2\dl,z+k_3\dl)), +\end{align*} +with +\begin{align*} + u &:= u_{0,000}, \\ + v &:= v_{0,000}, \\ + w &:= w_{0,000}. +\end{align*} +Negative subscript numbers are denoted by $\bar n:=-n$, $\forall n\in\mathbb{N}$, i.e., $\bar1:=-1$, $\bar2:=-2$, etc. + +\section{SRT} +\input{d3q7/supp_d3q7m0_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7n/d3q7m0n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7n/d3q7m0n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7n/d3q7m0n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7n/d3q7m0n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7n/d3q7m0n_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7n/d3q7m0n_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7n/d3q7m0n_efde6} + +\section{MRT 1: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$, $\mF$, $\mG$} +\input{d3q7/supp_d3q7m1_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7n/d3q7m1n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7n/d3q7m1n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7n/d3q7m1n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7n/d3q7m1n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7n/d3q7m1n_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7n/d3q7m1n_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7n/d3q7m1n_efde6} + +\section{MRT 2: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE+\mF+\mG$, $\mE-\mF$, $\mE-\mF$} +\input{d3q7/supp_d3q7m2_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7n/d3q7m2n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7n/d3q7m2n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7n/d3q7m2n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7n/d3q7m2n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7n/d3q7m2n_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7n/d3q7m2n_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7n/d3q7m2n_efde6} + +\section{MRT 3: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$, $\mF$, $\mG$} +\input{d3q7/supp_d3q7m3_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7n/d3q7m3n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7n/d3q7m3n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7n/d3q7m3n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7n/d3q7m3n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7n/d3q7m3n_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7n/d3q7m3n_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7n/d3q7m3n_efde6} + +\section{MRT 4: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE+\mF+\mG$, $\mE-\mF$, $\mE-\mF$} +\input{d3q7/supp_d3q7m4_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7n/d3q7m4n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7n/d3q7m4n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7n/d3q7m4n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7n/d3q7m4n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7n/d3q7m4n_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7n/d3q7m4n_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7n/d3q7m4n_efde6} + +\section{CLBM 1: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE$, $\kF$, $\kG$} +\input{d3q7/supp_d3q7m5_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7n/d3q7m5n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7n/d3q7m5n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7n/d3q7m5n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7n/d3q7m5n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7n/d3q7m5n_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7n/d3q7m5n_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7n/d3q7m5n_efde6} + +\section{CLBM 2: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE+\kF+\kG$, $\kE-\kF$, $\kE-\kG$} +\input{d3q7/supp_d3q7m6_defs.tex} +\subsection{EFDE for $\mmA$}\input{../output_D3Q7n/d3q7m6n_efde0} +\subsection{EFDE for $\mmB$}\input{../output_D3Q7n/d3q7m6n_efde1} +\subsection{EFDE for $\mmC$}\input{../output_D3Q7n/d3q7m6n_efde2} +\subsection{EFDE for $\mmD$}\input{../output_D3Q7n/d3q7m6n_efde3} +\subsection{EFDE for $\mmE$}\input{../output_D3Q7n/d3q7m6n_efde4} +\subsection{EFDE for $\mmF$}\input{../output_D3Q7n/d3q7m6n_efde5} +\subsection{EFDE for $\mmG$}\input{../output_D3Q7n/d3q7m6n_efde6} + +\end{document} + diff --git a/tex/supp_d3q7n_epde.tex b/tex/supp_d3q7n_epde.tex new file mode 100644 index 0000000000000000000000000000000000000000..c2c024e75b9b7e8360b8c49004521ca16f71aead --- /dev/null +++ b/tex/supp_d3q7n_epde.tex @@ -0,0 +1,84 @@ +\input{header} + +\titler{EPDE}{D3Q7}{variable velocities} + +\input{d3q7/d3q7_defs} + +\begin{document} +\maketitle +\tableofcontents + +\input{d3q7/supp_d3q7_defs} + +\section{SRT} +\input{d3q7/supp_d3q7m0_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7n/d3q7m0n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7n/d3q7m0n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7n/d3q7m0n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7n/d3q7m0n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7n/d3q7m0n_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7n/d3q7m0n_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7n/d3q7m0n_epde6} + +\section{MRT 1: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$, $\mF$, $\mG$} +\input{d3q7/supp_d3q7m1_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7n/d3q7m1n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7n/d3q7m1n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7n/d3q7m1n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7n/d3q7m1n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7n/d3q7m1n_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7n/d3q7m1n_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7n/d3q7m1n_epde6} + +\section{MRT 2: relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE+\mF+\mG$, $\mE-\mF$, $\mE-\mF$} +\input{d3q7/supp_d3q7m2_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7n/d3q7m2n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7n/d3q7m2n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7n/d3q7m2n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7n/d3q7m2n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7n/d3q7m2n_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7n/d3q7m2n_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7n/d3q7m2n_epde6} + +\section{MRT 3: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE$, $\mF$, $\mG$} +\input{d3q7/supp_d3q7m3_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7n/d3q7m3n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7n/d3q7m3n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7n/d3q7m3n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7n/d3q7m3n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7n/d3q7m3n_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7n/d3q7m3n_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7n/d3q7m3n_epde6} + +\section{MRT 4: with ortogonalization and relaxation of $\mA$, $\mB$, $\mC$, $\mD$, $\mE+\mF+\mG$, $\mE-\mF$, $\mE-\mF$} +\input{d3q7/supp_d3q7m4_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7n/d3q7m4n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7n/d3q7m4n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7n/d3q7m4n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7n/d3q7m4n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7n/d3q7m4n_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7n/d3q7m4n_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7n/d3q7m4n_epde6} + +\section{CLBM 1: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE$, $\kF$, $\kG$} +\input{d3q7/supp_d3q7m5_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7n/d3q7m5n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7n/d3q7m5n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7n/d3q7m5n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7n/d3q7m5n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7n/d3q7m5n_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7n/d3q7m5n_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7n/d3q7m5n_epde6} + +\section{CLBM 2: relaxation of $\kA$, $\kB$, $\kC$, $\kD$, $\kE+\kF+\kG$, $\kE-\kF$, $\kE-\kG$} +\input{d3q7/supp_d3q7m6_defs.tex} +\subsection{EPDE for $\mmA$}\input{../output_D3Q7n/d3q7m6n_epde0} +\subsection{EPDE for $\mmB$}\input{../output_D3Q7n/d3q7m6n_epde1} +\subsection{EPDE for $\mmC$}\input{../output_D3Q7n/d3q7m6n_epde2} +\subsection{EPDE for $\mmD$}\input{../output_D3Q7n/d3q7m6n_epde3} +\subsection{EPDE for $\mmE$}\input{../output_D3Q7n/d3q7m6n_epde4} +\subsection{EPDE for $\mmF$}\input{../output_D3Q7n/d3q7m6n_epde5} +\subsection{EPDE for $\mmG$}\input{../output_D3Q7n/d3q7m6n_epde6} + +\end{document} +