Simgrid selector called "runtime automatic switching"
(smpi/privatize\_global\_variables). Indeed, global variables can generate side
effects on runtime between the threads running in the same process, generated by
-Simgrid to simulate the grid environment. \RC{On vire cette phrase ?} \RCE {Si c'est la phrase d'avant sur les threads, je pense qu'on peut la retenir car c'est l'explication du pourquoi Simgrid n'aime pas les variables globales. Si c'est pas bien dit, on peut la reformuler. Si c'est la phrase ci-apres, effectivement, on peut la virer si elle preterais a discussion}The
-last modification on the MPI program pointed out for some cases, the review of
-the sequence of the MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions which
-might cause an infinite loop.
+Simgrid to simulate the grid environment.
+
+%\RC{On vire cette phrase ?} \RCE {Si c'est la phrase d'avant sur les threads, je pense qu'on peut la retenir car c'est l'explication du pourquoi Simgrid n'aime pas les variables globales. Si c'est pas bien dit, on peut la reformuler. Si c'est la phrase ci-apres, effectivement, on peut la virer si elle preterais a discussion}The
+%last modification on the MPI program pointed out for some cases, the review of
+%the sequence of the MPI\_Isend, MPI\_Irecv and MPI\_Waitall instructions which
+%might cause an infinite loop.
\paragraph{Simgrid Simulator parameters}
\item matrix diagonal value = 6.0 for synchronous Krylov multisplitting experiments and 6.2 for asynchronous block Jacobi experiments; \RC{CE tu vérifies, je dis ca de tête}
\item matrix off-diagonal value;
\item execution mode: synchronous or asynchronous;
- \RCE {C'est ok la liste des arguments du programme mais si Lilia ou toi pouvez preciser pour les arguments pour CGLS ci dessous}
+ \RCE {C'est ok la liste des arguments du programme mais si Lilia ou toi pouvez preciser pour les arguments pour CGLS ci dessous} \RC{Vu que tu n'as pas fait varier ce paramètre, on peut ne pas en parler}
\item Size of matrix S;
\item Maximum number of iterations and tolerance threshold for CGLS.
\end{itemize}
\section{Experimental Results}
\label{sec:expe}
-In this section, experiments for both Multisplitting algorithms are reported. First the problem used in our experiments is described.
+In this section, experiments for both Multisplitting algorithms are reported. First the 3D Poisson problem used in our experiments is described.
+
+\subsection{3D Poisson}
+
We use our two-stage algorithms to solve the well-known Poisson problem $\nabla^2\phi=f$~\cite{Polyanin01}. In three-dimensional Cartesian coordinates in $\mathbb{R}^3$, the problem takes the following form
\begin{equation}
speed. The network between distant clusters might be a bottleneck for the
global performance of the application.
-\subsection{Comparing GMRES and Multisplitting algorithms in
-synchronous mode}
+\subsection{Comparison of GMRES and Krylov Multisplitting algorithms in synchronous mode}
-In the scope of this paper, our first objective is to demonstrate the
-Algo-2 (Multisplitting method) shows a better performance in grid
-architecture compared with Algo-1 (Classical GMRES) both running in
-\textit{synchronous mode}. Better algorithm performance
-should means a less number of iterations output and a less 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 the targeted outcomes, particularly for poor and
-slow networks, focusing on the impact on the communication performance
-on the chosen class of algorithm.
+In the scope of this paper, our first objective is to analyze when the Krylov
+Multisplitting method has better performances than the classical GMRES
+method. With an iterative method, better performances mean 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 the targeted outcomes, particularly for poor
+and slow networks, focusing on the impact on the communication performance on
+the chosen class of algorithm.
The following paragraphs present the test conditions, the output results
and our comments.\\
-\textit{3.a Executing the algorithms on various computational grid
+\subsubsection{Execution of the the algorithms on various computational grid
architecture and scaling up the input matrix size}
-\\
-
+\ \\
% environment
-\begin{footnotesize}
+
+\begin{figure} [ht!]
+\begin{center}
\begin{tabular}{r c }
\hline
Grid & 2x16, 4x8, 4x16 and 8x8\\ %\hline
Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ %\hline
- & N$_{x}$ x N$_{y}$ x N$_{z}$ =170 x 170 x 170 \\ \hline
\end{tabular}
-Table 1 : Clusters x Nodes with N$_{x}$=150 or N$_{x}$=170 \\
+\caption{Clusters x Nodes with N$_{x}$=150 or N$_{x}$=170 \RC{je ne comprends pas la légende... Ca ne serait pas plutot Characteristics of cluster (mais il faudrait lui donner un nom)}}
+\end{center}
+\end{figure}
-\end{footnotesize}
%\RCE{J'ai voulu mettre les tableaux des données mais je pense que c'est inutile et ça va surcharger}
-In this section, we compare the algorithms performance running on various grid configuration (2x16, 4x8, 4x16 and 8x8). First, the results in figure 3 show for all grid configuration 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.
+In this section, we analyze the performences of algorithms running on various
+grid configuration (2x16, 4x8, 4x16 and 8x8). First, the results in Figure~\ref{fig:01}
+show for all grid configuration 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...}
+
-%\begin{wrapfigure}{l}{100mm}
\begin{figure} [ht!]
-\centering
-\includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
-\caption{Cluster x Nodes N$_{x}$=150 and N$_{x}$=170}
-%\label{overflow}}
+ \begin{center}
+ \includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
+ \end{center}
+ \caption{Cluster x Nodes N$_{x}$=150 and N$_{x}$=170}
+ \label{fig:01}
\end{figure}
-%\end{wrapfigure}
+
The execution time difference between the two algorithms is important when
comparing between different grid architectures, even with the same number of
