modif

diff --git a/paper.tex b/paper.tex
index a2e23a24ae4510982b193106b880884da634d8dc..9cc8e03242a2e922c46c77adb2f3f4dbefd68589 100644 (file)
--- 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
 \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. 
 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 \\}
 
 
 \subsubsection{Simulations for two different inter-clusters network speeds \\}