petites modifs 5.4.2

[rce2015.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 26f40cb3cc4b5886dfe1240c93b7b0737e8327d8..24ddab9a5181b4cac5b4f9e5264ebaa158981912 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -574,12 +574,15 @@ The execution times between both algorithms is significant with different grid a
 \end{figure}
 
 \subsubsection{Simulations for two different inter-clusters network speeds\\}
 \end{figure}
 
 \subsubsection{Simulations for two different inter-clusters network speeds\\}

-In Figure~\ref{fig:02} we present the execution times of both algorithms to solve a 3D Poisson problem of size $150^3$ on two different simulated network $N1$ and $N2$ (see Table~\ref{tab:01}). As it was previously said, we can see from the figure that the Krylov two-stage algorithm is more sensitive the number of clusters than the GMRES algorithm. However, we can notice an interesting behavior of the Krylov two-stage algorithm. It is less sensitive to bad network bandwidth and latency for the inter-clusters links than the GMRES algorithms. This means that the multisplitting methods are more efficient for distributed systems with high latency networks.
-
-
-
-
-%% The figure shows that the Krylov two-stage algorithm is more sensitive the number of clusters than the GMRES algorithm.
+In  Figure~\ref{fig:02} we  present the  execution times  of both  algorithms to
+solve a  3D Poisson problem of  size $150^3$ on two  different simulated network
+$N1$ and $N2$ (see Table~\ref{tab:01}). As previously mentioned, we can see from
+this figure  that the Krylov two-stage  algorithm is sensitive to  the number of
+clusters (i.e. it is better to have a small number of clusters). However, we can
+notice an  interesting behavior of  the Krylov  two-stage algorithm. It  is less
+sensitive to bad network bandwidth and latency for the inter-clusters links than
+the  GMRES algorithms.  This  means  that the  multisplitting  methods are  more
+efficient for distributed systems with high latency networks.

 
 %% In this section, the experiments  compare the  behavior of  the algorithms  running on a
 %% speeder inter-cluster  network (N2) and  also on  a less performant  network (N1) respectively defined in the test conditions Table~\ref{tab:02}.
 
 %% In this section, the experiments  compare the  behavior of  the algorithms  running on a
 %% speeder inter-cluster  network (N2) and  also on  a less performant  network (N1) respectively defined in the test conditions Table~\ref{tab:02}.


@@ -588,8 +591,6 @@ In Figure~\ref{fig:02} we present the execution times of both algorithms to solv
 %% for  both  algorithms when using  a  grid  architecture  like  4 $\times$ 16 or  8 $\times$ 8: the reduction factor is around $2$. The results depict  also that when
 %% the  network speed  drops down (variation of 12.5\%), the  difference between  the two Multisplitting algorithms execution times can reach more than 25\%.
 
 %% for  both  algorithms when using  a  grid  architecture  like  4 $\times$ 16 or  8 $\times$ 8: the reduction factor is around $2$. The results depict  also that when
 %% the  network speed  drops down (variation of 12.5\%), the  difference between  the two Multisplitting algorithms execution times can reach more than 25\%.
 

-\LZK{J'ai mis que le problème résolu dans la figure 4 est de taille $150^3$. CE, pourrais tu le confirmer?}
-

 \begin{figure}[t]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
 \begin{figure}[t]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}