\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}.
%% 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}
in Table~\ref{tab:07}. In order to compare the execution times, this table
reports the relative gain between both algorithms. It is defined by the ratio
between the execution time of GMRES and the execution time of the
-multisplitting. The ration is greater than one because the asynchronous
+multisplitting. The ratio is greater than one because the asynchronous
multisplitting version is faster than GMRES.
