@@ -141,7 +141,7 @@ The following parameters were set specifically for GPU computations:
\item The local interpolation transposes were saved to avoid sparse matrix--transpose--vector multiplications: \ic{HYPRE_BoomerAMGSetKeepTranspose( precond, 1 );}
\item The triple matrix product $\matrix R \matrix A \matrix P$ was replaced by two matrix products: \\\ic{HYPRE_BoomerAMGSetRAP2( precond, 1 );}
\end{itemize}
There are many other configurable parameters listed in the Hypre manual \cite{Hypre:manual} that might have an effect on the performance, but they were not investigated in this benchmark.
There are many other configurable parameters listed in the Hypre documentation \cite{Hypre:documentation} that might have an effect on the performance, but they were not investigated in this benchmark.
To reduce the computational time with the Hypre implementation, the BoomerAMG preconditioner is not updated in every time step and instead its setup is reused multiple times as long as the number of iterations necessary for the BiCGstab method to converge does not increase significantly.
Reusing preconditioners and recycling Krylov subspaces are common techniques for solving sequences of linear systems \cite{carr2021recycling,amritkar2015recycling,gaul2014recycling}, such as those arising from discretizations of evolutionary partial differential equations.
author={Monakov, Alexander and Lokhmotov, Anton and Avetisyan, Arutyun},
booktitle={High Performance Embedded Architectures and Compilers},
publisher={Springer},
series={Lecture Notes in Computer Science},
volume={5952},
publisher={Springer, Berlin, Heidelberg},
title={Automatically tuning sparse matrix-vector multiplication for {GPU} architectures},
year={2010},
pages={111--125},
@@ -132,12 +132,11 @@
publisher={SIAM},
}
@Misc{spatial,
@Online{spatial,
author={Sylvain Bougerel},
note={[Online; accessed November 2017]},
note={[Accessed November 2017]},
title={Spatial {C++} library -- Library of generic, k-d tree multi-dimensional containers},
year={2017},
keywords={online},
url={https://sourceforge.net/projects/spatial/},
}
@@ -183,12 +182,11 @@
publisher={Elsevier},
}
@Misc{VCGlib,
@Online{VCGlib,
author={Paolo Cignoni and Fabio Ganovelli},
note={[Online; accessed November 2017]},
note={[Accessed November 2017]},
title={{Visualization and Computer Graphics Library (VCGlib)}},
year={2017},
keywords={online},
url={http://vcg.isti.cnr.it/vcglib/},
}
@@ -200,7 +198,7 @@
publisher={Kitware},
}
@InCollection{ahrens:2005paraview,
@InBook{ahrens:2005paraview,
author={Ahrens, James and Geveci, Berk and Law, Charles},
booktitle={Visualization Handbook},
publisher={Butterworth-Heinemann},
@@ -214,7 +212,7 @@
doi={10.1016/b978-012387582-2/50038-1},
}
@InCollection{HPV:VisIt,
@InBook{HPV:VisIt,
author={Hank Childs and Eric Brugger and Brad Whitlock and Jeremy Meredith and Sean Ahern and David Pugmire and Kathleen Biagas and Mark Miller and Cyrus Harrison and Gunther H. Weber and Hari Krishnan and Thomas Fogal and Allen Sanderson and Christoph Garth and E. Wes Bethel and David Camp and Oliver R\"{u}bel and Marc Durant and Jean M. Favre and Paul Navr\'{a}til},