From b86c85516c6889f5d743154ed489941a59ae307b Mon Sep 17 00:00:00 2001 From: couturie Date: Sat, 19 Sep 2015 11:22:20 +0200 Subject: [PATCH] new --- IJHPCN/paper.tex | 70 +++++++++++++++++++++--------------------------- 1 file changed, 30 insertions(+), 40 deletions(-) diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex index 21fa922..4c711cc 100644 --- a/IJHPCN/paper.tex +++ b/IJHPCN/paper.tex @@ -776,25 +776,6 @@ taken into account with TSIRM. \end{figure} -Concerning the experiments some other remarks are interesting. -\begin{itemize} -\item We have tested other examples of PETSc/KSP (ex29, ex45, ex49). For all these - examples, we have also obtained similar gains between GMRES and TSIRM but - those examples are not scalable with many cores. In general, we had some - problems with more than $4,096$ cores. -\item We have tested many iterative solvers available in PETSc. In fact, it is - possible to use most of them with TSIRM. From our point of view, the condition - to use a solver inside TSIRM is that the solver must have a restart - feature. More precisely, the solver must support to be stopped and restarted - without decreasing its convergence. That is why with GMRES we stop it when it - is naturally restarted (\emph{i.e.} with $m$ the restart parameter). The - Conjugate Gradient (CG) and all its variants do not have ``restarted'' version - in PETSc, so they are not efficient. They will converge with TSIRM but not - quickly because if we compare a normal CG with a CG which is stopped and - restarted every 16 iterations (for example), the normal CG will be far more - efficient. Some restarted CG or CG variant versions exist and may be - interesting to study in future works. -\end{itemize} %%%********************************************************* %%%********************************************************* @@ -803,26 +784,6 @@ Concerning the experiments some other remarks are interesting. \subsection{Nonlinear problems in parallel} -\begin{table*}[htbp] -\begin{center} -\begin{tabular}{|r|r|r|r|r|r|r|r|} -\hline - - nb. cores & \multicolumn{2}{c|}{FGMRES/ASM} & \multicolumn{2}{c|}{TSIRM CGLS/ASM} & gain& \multicolumn{2}{c|}{FGMRES/HYPRE} \\ -\cline{2-5} \cline{7-8} - & Time & \# Iter. & Time & \# Iter. & & Time & \# Iter. \\\hline \hline - 512 & 5.54 & 685 & 2.5 & 570 & 2.21 & 128.9 & 9 \\ - 2048 & 14.95 & 1,560 & 4.32 & 746 & 3.48 & 335.7 & 9 \\ - 4096 & 25.13 & 2,369 & 5.61 & 859 & 4.48 & >1000 & -- \\ - 8192 & 44.35 & 3,197 & 7.6 & 1083 & 5.84 & >1000 & -- \\ - -\hline - -\end{tabular} -\caption{Comparison of FGMRES and TSIRM for ex45 of PETSc/KSP with two preconditioner (ASM and HYPRE) having 25,000 components per core on Curie ($\epsilon_{tsirm}=1e-10$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$), time is expressed in seconds.} -\label{tab:06} -\end{center} -\end{table*} \begin{figure}[htbp] @@ -877,10 +838,39 @@ Concerning the experiments some other remarks are interesting. \end{table*} -\subsection{Influcence of parameters for TSIRM} +\subsection{Influence of parameters for TSIRM} + + + + + +\subsection{Experiments conclusions } + +{\bf A refaire} + +Concerning the experiments some other remarks are interesting. +\begin{itemize} +\item We have tested other examples of PETSc/KSP (ex29, ex45, ex49). For all these + examples, we have also obtained similar gains between GMRES and TSIRM but + those examples are not scalable with many cores. In general, we had some + problems with more than $4,096$ cores. +\item We have tested many iterative solvers available in PETSc. In fact, it is + possible to use most of them with TSIRM. From our point of view, the condition + to use a solver inside TSIRM is that the solver must have a restart + feature. More precisely, the solver must support to be stopped and restarted + without decreasing its convergence. That is why with GMRES we stop it when it + is naturally restarted (\emph{i.e.} with $m$ the restart parameter). The + Conjugate Gradient (CG) and all its variants do not have ``restarted'' version + in PETSc, so they are not efficient. They will converge with TSIRM but not + quickly because if we compare a normal CG with a CG which is stopped and + restarted every 16 iterations (for example), the normal CG will be far more + efficient. Some restarted CG or CG variant versions exist and may be + interesting to study in future works. +\end{itemize} %%ENDNEW + %%%********************************************************* %%%********************************************************* \section{Conclusion} -- 2.39.5