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\section{Simulation of the multisplitting method}
+
+\subsection{The multisplitting method}
%Décrire le problème (algo) traité ainsi que le processus d'adaptation à SimGrid.
Let $Ax=b$ be a large sparse system of $n$ linear equations in $\mathbb{R}$, where $A$ is a sparse square and nonsingular matrix, $x$ is the solution vector and $b$ is the right-hand side vector. We use a multisplitting method based on the block Jacobi splitting to solve this linear system on a large scale platform composed of $L$ clusters of processors~\cite{o1985multi}. In this case, we apply a row-by-row splitting without overlapping
\begin{equation*}
\end{figure}
+\subsection{Simulation of the multisplitting method using SimGrid and SMPI}
+
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\begin{itemize}
\item HOSTFILE: Text file containing the list of the processors units name. Here 100 hosts;
-\item PLATFORM: XML file description of the platform architecture : two clusters (cluster1 and cluster2) with the following characteristics :
+\item PLATFORM: XML file description of the platform architecture whith the following characteristics: %two clusters (cluster1 and cluster2) with the following characteristics :
\begin{itemize}
+ \item 2 clusters of 50 hosts each;
\item Processor unit power: \np[GFlops]{1.5};
\item Intracluster network bandwidth: \np[Gbit/s]{1.25} and latency:
\np[$\mu$s]{0.05};
\begin{itemize}
\item Description of the cluster architecture matching the format <Number of
- cluster> <Number of hosts in cluster1> <Number of hosts in cluster2>;
+ clusters> <Number of hosts in cluster1> <Number of hosts in cluster2>;
\item Maximum number of iterations;
\item Precisions on the residual error;
\item Matrix size $N_x$, $N_y$ and $N_z$;
-\item Matrix diagonal value: $6$ (See~(\ref{eq:03}));
+\item Matrix diagonal value: $6$ (See Equation~(\ref{eq:03}));
\item Matrix off-diagonal value: $-1$;
\item Communication mode: asynchronous.
\end{itemize}
