inter-cluster communications. In the following, these parameters are described:
\begin{itemize}
- \item hostfile: hosts description file.
+ \item hostfile: hosts description file,
\item platform: file describing the platform architecture: clusters (CPU power,
\dots{}), intra cluster network description, inter cluster network (bandwidth $bw$,
-latency $lat$, \dots{}).
+latency $lat$, \dots{}),
\item archi : grid computational description (number of clusters, number of
nodes/processors in each cluster).
\end{itemize}
on the one hand the algorithm execution mode (synchronous and asynchronous)
and on the other hand the execution time and the number of iterations to reach the convergence. \\
-\textbf{Step 4 }: Set up the different grid testbed environments that will be
+\textbf{Step 4}: Set up the different grid testbed environments that will be
simulated in the simulator tool to run the program. The following architectures
have been configured in SimGrid : 2$\times$16, 4$\times$8, 4$\times$16, 8$\times$8 and 2$\times$50. The first number
represents the number of clusters in the grid and the second number represents
(resp. inter-clusters backbone links). \\
\LZK{Il me semble que le bw et lat des deux réseaux varient dans les expés d'une simu à l'autre. On vire la dernière phrase?}
+\RC{il me semble qu'on peut laisser ca}
\textbf{Step 5}: Conduct an extensive and comprehensive testings
within these configurations by varying the key parameters, especially
In the scope of this paper, our first objective is to analyze when the Krylov
two-stage method has better performance than the classical GMRES method. With a synchronous iterative method, better performance means a
smaller number of iterations and execution time before reaching the convergence.
-For a systematic study, the experiments should figure out that, for various
-grid parameters values, the simulator will confirm Multisplitting method better performance compared to classical GMRES, particularly on poor and slow networks.
-\LZK{Pas du tout claire la dernière phrase (For a systematic...)!!}
-\RCE { Reformule autrement}
+In what follows, we will present the test conditions, the output results and our comments.
+
+%%RAPH : on vire ca, c'est pas clair et pas important
+%For a systematic study, the experiments should figure out that, for various
+%grid parameters values, the simulator will confirm Multisplitting method better performance compared to classical GMRES, particularly on poor and slow networks.
+%\LZK{Pas du tout claire la dernière phrase (For a systematic...)!!}
+%\RCE { Reformule autrement}
+
-In what follows, we will present the test conditions, the output results and our comments.\\
%\subsubsection{Execution of the algorithms on various computational grid architectures and scaling up the input matrix size}
\subsubsection{Simulations for various grid architectures and scaling-up matrix sizes}
\ \\
% environment
+\RC{Je ne comprends plus rien CE : pourquoi dans 5.4.1 il y a 2 network et aussi dans 5.4.2. Quelle est la différence? Dans la figure 3 de la section 5.4.1 pourquoi il n'y a pas N1 et N2?}
+
\begin{table} [ht!]
\begin{center}
\begin{tabular}{ll }
& N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$ =170 $\times$ 170 $\times$ 170 \\ \hline
\end{tabular}
\caption{Test conditions: various grid configurations with the matrix sizes 150$^3$ or 170$^3$}
-\LZK{Ce sont les caractéristiques du réseau intra ou inter clusters? Ce n'est pas précisé...}
-\RCE{oui c est precise}
+%\LZK{Ce sont les caractéristiques du réseau intra ou inter clusters? Ce n'est pas précisé...}
+%\RCE{oui c est precise}
\label{tab:01}
\end{center}
\end{table}
-In this section, we analyze the simulations conducted on various grid configurations presented in Table~\ref{tab:01}. Figure~\ref{fig:01} shows, for all grid configurations and a given matrix size, 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 presented in Table~\ref{tab:01}. It should be noticed that two
+networks are considered: N1 is the network between clusters (inter-cluster) and
+N2 is the network inside a cluster (intra-cluster). Figure~\ref{fig:01} shows,
+for all grid configurations and a given matrix size, a non-variation in the
+number of iterations for the classical GMRES algorithm, which is not the case of
+the Krylov two-stage algorithm.
%% First, the results in Figure~\ref{fig:01}
%% show for all grid configurations the non-variation of the number of iterations of
%% classical GMRES for a given input matrix size; it is not the case for the
%% multisplitting method.
-\RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}
-\RC{Les légendes ne sont pas explicites...}
-\RCE{Corrige}
+%\RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}
+%\RC{Les légendes ne sont pas explicites...}
+%\RCE{Corrige}
\begin{figure} [ht!]
\begin{center}
\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$^3$
-\AG{Utiliser le point comme séparateur décimal et non la virgule. Idem dans les autres figures.}}
-\LZK{Pour quelle taille du problème sont calculés les nombres d'itérations? Que représente le 2 Clusters x 16 Nodes with Nx=150 and Nx=170 en haut de la figure?}
-\RCE {Corrige}
+ \caption{Various grid configurations with the matrix sizes 150$^3$ and 170$^3$}
+%\AG{Utiliser le point comme séparateur décimal et non la virgule. Idem dans les autres figures.}
+%\LZK{Pour quelle taille du problème sont calculés les nombres d'itérations? Que représente le 2 Clusters x 16 Nodes with Nx=150 and Nx=170 en haut de la figure?}
+ %\RCE {Corrige}
+ \RC{Idéalement dans la légende il faudrait insiquer Pb size=$150^3$ ou $170^3$ car pour l'instant Nx=150 ca n'indique rien concernant Ny et Nz}
\label{fig:01}
\end{figure}
+
+
The execution times between the two 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
\end{table}
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...}
+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\%.
