reorganized notes for the linear systems chapter (d3aa6974) · Commits · Jakub Klinkovský / Dissertation

content/document.tex

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		@@ -56,27 +56,9 @@ In this chapter, we present several data structures which are flexible in the se
		\input{content/meshes/meshes.tex}

		\cleardoublepage
		\chapter{Iterative Methods for Sparse Linear Systems}
		\chapter{Solution of Sparse Linear Systems}
		\label{chapter:linear systems}

		\inline{No supporting paper since the CWY-GMRES paper was discarded...}
		\inline{discuss left-preconditioning vs right-preconditioning}

		\section{Distributed sparse matrix--vector multiplication}

		\inline{Description will depend on the distributed mesh (ghost regions)}

		\section{CWY--GMRES}

		\inline{???}

		\section{BiCGstab}

		\inline{???}

		\section{Hypre solvers (state of the art)}

		\inline{??? (zde by byla jen rešerše + stručný popis wrapperů v TNL)}
		\input{content/linear_systems.tex}

		\cleardoublepage
		\chapter{Numerical Methods for Computational Fluid Dynamics}

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		\inline{No supporting paper since the CWY-GMRES paper was discarded...}
		\inline{mention direct methods vs iterative methods in the intro}

		\section{Iterative methods}
		\inline{make a summary of the state of the art}
		\inline{stopping criteria?}

		\section{Preconditioning techniques}
		\inline{general intro, discuss left-preconditioning vs right-preconditioning}
		\inline{make a summary of the state of the art}

		\section{Software packages}
		\inline{incomplete list of notable software which implements iterative methods or preconditioners -- features and development status}
		\inline{state of the art: Hypre}
		\inline{TNL status}

		\section{Distributed sparse matrix}

		\inline{introduce the section in the context of the chapter}

		The implementation of a distributed sparse matrix in TNL is closely bound to the distributed mesh described in \cref{sec:meshes:distributed}.
		\inline{Description will depend on the distributed mesh (ghost regions)}
		\inline{Distributed sparse matrix--vector multiplication}

		The implementation of a distributed sparse matrix in the Hypre library \cite{Hypre:library,Hypre:design1,Hypre:design2} is different from TNL in several aspects.
		\inline{explain the assumed partition scheme}
		\inline{describe the conventions used in the \texttt{hypre\_CSRMatrix} (the diagonal entry in each row is stored in the first place in the CSR format)}
		\inline{describe the \texttt{hypre\_ParCSRMatrix} format (\ic{diag}, \ic{offd}, \texttt{col\_map\_offd})}