+
+%%% AJOUTE ************************
+%%%********************************
+We have performed some experiments on an infiniband cluster of three Intel Xeon
+quad-core E5620 CPUs of 2.40 GHz and 12 GB of memory. For the GMRES code (alone
+and in both multisplitting versions) the restart parameter is fixed to 16. The
+precision of the GMRES version is fixed to 1e-6. For the multisplitting
+versions, there are two precisions, one for the external solver which is fixed
+to 1e-6 and another one for the inner solver (GMRES) which is fixed to 1e-10. It
+should be noted that a high precision is used but we also fixed a maximum number
+of iterations for each internal step. In practice, we limit the number of
+iterations in the internal step to 10. So an internal iteration is finished when
+the precision is reached or when the maximum internal number of iterations is
+reached. The precision and the maximum number of iterations of CGNR method used
+by our Krylov multisplitting algorithm are fixed to 1e-25 and 20
+respectively. The size of the Krylov subspace basis $S$ is fixed to 10 vectors.
+
+\begin{figure}[htbp]
+\centering
+ \includegraphics[width=0.8\textwidth]{strong_scaling_150x150x150}
+\caption{Strong scaling with 3 blocks of 4 cores each to solve a 3D Poisson problem of size $150^3$ components}
+\label{fig:001}
+\end{figure}
+
+\begin{figure}[htbp]
+\centering
+\begin{tabular}{c}
+\includegraphics[width=0.8\textwidth]{weak_scaling_280k} \\ \includegraphics[width=0.8\textwidth]{weak_scaling_280K2}\\
+\end{tabular}
+\caption{Weak scaling with 3 blocks of 4 cores each to solve a 3D Poisson problem with approximately 280K components per core}
+\label{fig:002}
+\end{figure}
+
+%%The experiments are performed on 3 different clusters of cores interconnected by an infiniband network (each cluster is a quad-core CPU).
+Figures~\ref{fig:001} and~\ref{fig:002} show the scalability performances of
+GMRES, classical multisplitting and Krylov multisplitting methods: strong and
+weak scaling are presented respectively. We can remark from these figures that
+the performances of our Krylov multisplitting method are better than those of
+GMRES and classical multisplitting methods. In the experiments conducted in this
+work, our method is approximately twice faster than the GMRES method and about 9
+times faster than the classical multisplitting method. Our multisplitting method
+uses a minimization step over a Krylov subspace which reduces the number of
+iterations and accelerates the convergence. We can also remark that the
+performances of the classical block Jacobi multisplitting method are the worst
+compared with those of the other two methods. This is why in the following
+experiments we compare the performances of our Krylov multisplitting method with
+only those of the GMRES method.
+%%%********************************
+%%%********************************
+
+
+%%% MODIFIE ************************
+%%%*********************************
