From 10e29ec6c99b9f2d163484f8e73c99adcfb8ed1d Mon Sep 17 00:00:00 2001 From: couturie Date: Fri, 8 May 2015 12:49:36 +0200 Subject: [PATCH] modif --- paper.tex | 19 ++++++++++++++----- 1 file changed, 14 insertions(+), 5 deletions(-) diff --git a/paper.tex b/paper.tex index a2e23a2..9cc8e03 100644 --- a/paper.tex +++ b/paper.tex @@ -552,7 +552,16 @@ Grid architecture & 2$\times$16, 4$\times$8, 4$\times$16 a \subsubsection{Simulations for various grid architectures and scaling-up matrix sizes} \ \\ % environment -In this section, we analyze the simulations conducted on various grid configurations and for different sizes of the 3D Poisson problem. The parameters of the network between clusters is fixed to $N1$ (see Table~\ref{tab:01}. Figure~\ref{fig:01} shows, for all grid configurations and a given matrix size 170$^3$ elements, a non-variation in the number of iterations for the classical GMRES algorithm, which is not the case of the Krylov two-stage algorithm. +In this section, we analyze the simulations conducted on various grid +configurations and for different sizes of the 3D Poisson problem. The parameters +of the network between clusters is fixed to $N1$ (see +Table~\ref{tab:01}. Figure~\ref{fig:01} shows, for all grid configurations and a +given matrix size 170$^3$ elements, a non-variation in the number of iterations +for the classical GMRES algorithm, which is not the case of the Krylov two-stage +algorithm. In fact, with multisplitting algorithms, the number of splitting (in +our case, it is the number of clusters) influences on the convergence speed. The +higher the number of splitting is, the slower the convergence of the algorithm +is. @@ -594,15 +603,15 @@ In this section, we analyze the simulations conducted on various grid configurat -The execution times between the two algorithms is significant with different +The execution times between both algorithms is significant with different grid architectures, even with the same number of processors (for example, 2 $\times$ 16 and 4 $\times 8$). We can observe a better sensitivity of the Krylov multisplitting method (compared with the classical GMRES) when scaling up the number of the processors in the grid: in average, the GMRES (resp. Multisplitting) algorithm performs $40\%$ better (resp. $48\%$) when running from 32 (grid 2 $\times$ 16) to 64 processors/cores (grid 8 $\times$ 8). Note that even with a grid 8 $\times$ 8 having the maximum number of clusters, the execution time of the multisplitting method is in average 32\% less compared to GMRES. -\RC{pas très clair, c'est pas précis de dire qu'un algo perform mieux qu'un autre, selon quel critère?} -\LZK{A revoir toute cette analyse... Le multi est plus performant que GMRES. Les temps d'exécution de multi sont sensibles au nombre de CLUSTERS. Il est moins performant pour un nombre grand de cluster. Avez vous d'autres remarques?} -\RCE{Remarquez que meme avec une grille 8x8, le multi est toujours plus performant} +%\RC{pas très clair, c'est pas précis de dire qu'un algo perform mieux qu'un autre, selon quel critère?} +%\LZK{A revoir toute cette analyse... Le multi est plus performant que GMRES. Les temps d'exécution de multi sont sensibles au nombre de CLUSTERS. Il est moins performant pour un nombre grand de cluster. Avez vous d'autres remarques?} +%\RCE{Remarquez que meme avec une grille 8x8, le multi est toujours plus performant} \subsubsection{Simulations for two different inter-clusters network speeds \\} -- 2.39.5