From a1ff3fa3715cb0844074d7927cd852f6e0cb6b3f Mon Sep 17 00:00:00 2001 From: raphael couturier Date: Mon, 13 Oct 2014 10:09:54 +0200 Subject: [PATCH] new --- paper.tex | 27 +++++++++++++-------------- 1 file changed, 13 insertions(+), 14 deletions(-) diff --git a/paper.tex b/paper.tex index a7d529d..e93737c 100644 --- a/paper.tex +++ b/paper.tex @@ -873,16 +873,15 @@ Core(TM) i7-3630QM CPU @ 2.40GHz with the version 3.5.1 of PETSc. In Table~\ref{tab:02}, some experiments comparing the solving of the linear -systems obtained with the previous matrices with a GMRES variant and with out 2 -stage algorithm are given. In the second column, it can be noticed that either -GRMES or FGMRES (Flexible GMRES)~\cite{Saad:1993} is used to solve the linear -system. According to the matrices, different preconditioner is used. With -TSIRM, the same solver and the same preconditionner are used. This Table shows -that TSIRM can drastically reduce the number of iterations to reach the -convergence when the number of iterations for the normal GMRES is more or less -greater than 500. In fact this also depends on tow parameters: the number of -iterations to stop GMRES and the number of iterations to perform the -minimization. +systems obtained with the previous matrices with a GMRES variant and with TSIRM +are given. In the second column, it can be noticed that either GRMES or FGMRES +(Flexible GMRES)~\cite{Saad:1993} is used to solve the linear system. According +to the matrices, different preconditioner is used. With TSIRM, the same solver +and the same preconditionner are used. This Table shows that TSIRM can +drastically reduce the number of iterations to reach the convergence when the +number of iterations for the normal GMRES is more or less greater than 500. In +fact this also depends on tow parameters: the number of iterations to stop GMRES +and the number of iterations to perform the minimization. \begin{table}[htbp] @@ -973,7 +972,7 @@ preconditioner in PETSc please consult~\cite{petsc-web-page}. \hline \end{tabular} -\caption{Comparison of FGMRES and TSIRM with FGMRES for example ex15 of PETSc with two preconditioners (mg and sor) with 25,000 components per core on Juqueen (threshold 1e-3, restart=30, s=12), time is expressed in seconds.} +\caption{Comparison of FGMRES and TSIRM with FGMRES for example ex15 of PETSc with two preconditioners (mg and sor) with 25,000 components per core on Juqueen ($\epsilon_{tsirm}=1e-3$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$), time is expressed in seconds.} \label{tab:03} \end{center} \end{table*} @@ -1028,7 +1027,7 @@ the number of iterations. So, the overall benefit of using TSIRM is interesting. \begin{tabular}{|r|r|r|r|r|r|r|r|r|} \hline - nb. cores & threshold & \multicolumn{2}{c|}{FGMRES} & \multicolumn{2}{c|}{TSIRM CGLS} & \multicolumn{2}{c|}{TSIRM LSQR} & best gain \\ + nb. cores & $\epsilon_{tsirm}$ & \multicolumn{2}{c|}{FGMRES} & \multicolumn{2}{c|}{TSIRM CGLS} & \multicolumn{2}{c|}{TSIRM LSQR} & best gain \\ \cline{3-8} & & Time & \# Iter. & Time & \# Iter. & Time & \# Iter. & \\\hline \hline 2,048 & 8e-5 & 108.88 & 16,560 & 23.06 & 3,630 & 22.79 & 3,630 & 4.77 \\ @@ -1041,7 +1040,7 @@ the number of iterations. So, the overall benefit of using TSIRM is interesting. \hline \end{tabular} -\caption{Comparison of FGMRES and TSIRM with FGMRES algorithms for ex54 of Petsc (both with the MG preconditioner) with 25,000 components per core on Curie (restart=30, s=12), time is expressed in seconds.} +\caption{Comparison of FGMRES and TSIRM with FGMRES algorithms for ex54 of Petsc (both with the MG preconditioner) with 25,000 components per core on Curie ($max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$), time is expressed in seconds.} \label{tab:04} \end{center} \end{table*} @@ -1099,7 +1098,7 @@ taken into account with TSIRM. \hline \end{tabular} -\caption{Comparison of FGMRES and TSIRM with FGMRES for ex54 of Petsc (both with the MG preconditioner) with 204,919,225 components on Curie with different number of cores (restart=30, s=12, threshold 5e-5), time is expressed in seconds.} +\caption{Comparison of FGMRES and TSIRM with FGMRES for ex54 of Petsc (both with the MG preconditioner) with 204,919,225 components on Curie with different number of cores ($\epsilon_{tsirm}=5e-5$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$), time is expressed in seconds.} \label{tab:05} \end{center} \end{table*} -- 2.39.5