X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/538afc25a7a90630d2f90891d0a4d700bfe3460f..10e29ec6c99b9f2d163484f8e73c99adcfb8ed1d:/paper.tex

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 trÃ¨s clair, c'est pas prÃ©cis de dire qu'un algo perform mieux qu'un autre, selon quel critÃ¨re?}
-\LZK{A revoir toute cette analyse... Le multi est plus performant que GMRES. Les temps d'exÃ©cution 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 trÃ¨s clair, c'est pas prÃ©cis de dire qu'un algo perform mieux qu'un autre, selon quel critÃ¨re?}
+%\LZK{A revoir toute cette analyse... Le multi est plus performant que GMRES. Les temps d'exÃ©cution 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 \\}
 
