\end{center}
\end{table}
-\subsubsection{Simulations for various grid architectures and scaling-up matrix sizes}
-\ \\
-% environment
+\subsubsection{Simulations for various grid architectures and scaling-up matrix sizes\\}
+
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 $N2$ (see
\includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
\end{center}
\caption{Various grid configurations with the matrix sizes 150$^3$ and 170$^3$}
+\LZK{CE, la légende de la Figure 3 est trop large. Remplacer les N$_x\times$N$_y\times$N$_z$ par $Mat1$=150$^3$ et $Mat2$=170$^3$ comme dans la Table 1}
\label{fig:01}
\end{figure}
-\subsubsection{Simulations for two different inter-clusters network speeds \\}
-
-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}.
-%\RC{Il faut définir cela avant...}
-Figure~\ref{fig:02} shows that end users will reduce the execution time
-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\%.
+\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 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}.
+%% %\RC{Il faut définir cela avant...}
+%% Figure~\ref{fig:02} shows that end users will reduce the execution time
+%% 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\%.
\begin{figure}[t]
\centering
\includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
\caption{Various grid configurations with networks $N1$ vs. $N2$}
+\LZK{CE, remplacer les ``,'' des décimales par un ``.''}
\label{fig:02}
\end{figure}
-\subsubsection{Network latency impacts on performance}
-\ \\
+
+
+
+
+
+
+
+
+
+
+
+
+
+\subsubsection{Network latency impacts on performance\\}
+
\begin{table} [ht!]
\centering
\begin{tabular}{r c }
decreasing from $8.10^{-6}$ to $6.10^{-5}$ second.
-\subsubsection{Network bandwidth impacts on performance}
-\ \\
+\subsubsection{Network bandwidth impacts on performance\\}
+
\begin{table} [ht!]
\centering
\begin{tabular}{r c }
presents a better performance in the considered bandwidth interval with a gain
of $40\%$ which is only around $24\%$ for the classical GMRES.
-\subsubsection{Input matrix size impacts on performance}
-\ \\
+\subsubsection{Input matrix size impacts on performance\\}
+
\begin{table} [ht!]
\centering
\begin{tabular}{r c }
