tune their application for a given multi-core architecture. To show the validity
of this approach we first compare the simulated execution of the multisplitting
algorithm with the GMRES (Generalized Minimal Residual)
-solver~\cite{saad86} in synchronous mode. The obtained results on different
+solver~\cite{saad86} in synchronous mode.
+
+\LZK{Pas trop convainquant comme argument pour valider l'approche de simulation. \\On peut dire par exemple: on a pu simuler différents algos itératifs à large échelle (le plus connu GMRES et deux variantes de multisplitting) et la simulation nous a permis (sans avoir le vrai matériel) de déterminer quelle serait la meilleure solution pour une telle configuration de l'archi ou vice versa.\\A revoir...}
+
+The obtained results on different
simulated multi-core architectures confirm the real results previously obtained
-on non simulated architectures. We also confirm the efficiency of the
-asynchronous multisplitting algorithm compared to the synchronous GMRES. In
+on non simulated architectures.
+
+\LZK{Il n y a pas dans la partie expé cette comparaison et confirmation des résultats entre la simulation et l'exécution réelle des algos sur les vrais clusters.\\ Sinon on pourrait ajouter dans la partie expé une référence vers le journal supercomput de krylov multi pour confirmer que cette méthode est meilleure que GMRES sur les clusters large échelle.}
+
+We also confirm the efficiency of the
+asynchronous multisplitting algorithm compared to the synchronous GMRES.
+
+\LZK{P.S.: Pour tout le papier, le principal objectif n'est pas de faire des comparaisons entre des méthodes itératives!!\\Sinon, les deux algorithmes Krylov multisplitting synchrone et multisplitting asynchrone sont plus efficaces que GMRES sur des clusters à large échelle.\\Et préciser, si c'est vraiment le cas, que le multisplitting asynchrone est plus efficace et adapté aux clusters distants par rapport aux deux autres algos (je n'ai pas encore lu la partie expé)}
+
+In
this way and with a simple computing architecture (a laptop) SimGrid allows us
to run a test campaign of a real parallel iterative applications on
different simulated multi-core architectures. To our knowledge, there is no
experimental results are presented in section~\ref{sec:expe} followed by some
concluding remarks and perspectives.
+\LZK{Proposition d'un titre pour le papier: Grid-enabled simulation of large-scale linear iterative solvers.}
+
\section{The asynchronous iteration model and the motivations of our work}
\label{sec:asynchro}
A_{\ell\ell} x_\ell = c_\ell,\mbox{~for~}\ell=1,\ldots,L,
\label{eq:03}
\end{equation}
-where right-hand sides $c_\ell=b_\ell-\sum_{m\neq\ell}A_{\ell m}x_m$ are computed using the shared vectors $x_m$. In this paper, we use the well-known iterative method GMRES ({\it Generalized Minimal RESidual})~\cite{saad86} as an inner iteration to approximate the solutions of the different splittings arising from the block Jacobi multisplitting of matrix $A$. The algorithm in Figure~\ref{01} shows the main key points of our block Jacobi two-stage method executed by a cluster of processors. In line~\ref{solve}, the linear sub-system~(\ref{eq:03}) is solved in parallel using GMRES method where $\MIG$ and $\TOLG$ are the maximum number of inner iterations and the tolerance threshold for GMRES respectively. The convergence of the two-stage multisplitting methods, based on synchronous or asynchronous iterations, has been studied by many authors for example~\cite{Bru95,bahi07}.
+where right-hand sides $c_\ell=b_\ell-\sum_{m\neq\ell}A_{\ell m}x_m$ are computed using the shared vectors $x_m$. In this paper, we use the well-known iterative method GMRES ({\it Generalized Minimal RESidual})~\cite{saad86} as an inner iteration to approximate the solutions of the different splittings arising from the block Jacobi multisplitting of matrix $A$. The algorithm in Figure~\ref{alg:01} shows the main key points of our block Jacobi two-stage method executed by a cluster of processors. In line~\ref{solve}, the linear sub-system~(\ref{eq:03}) is solved in parallel using GMRES method where $\MIG$ and $\TOLG$ are the maximum number of inner iterations and the tolerance threshold for GMRES respectively. The convergence of the two-stage multisplitting methods, based on synchronous or asynchronous iterations, has been studied by many authors for example~\cite{Bru95,bahi07}.
\begin{figure}[t]
%\begin{algorithm}[t]
