13-12-2014 v00

[Krylov_multi.git] / krylov_multi_reviewed.tex

diff --git a/krylov_multi_reviewed.tex b/krylov_multi_reviewed.tex
index 13341729f3ecf6e0745187fba72aeae51cd9318d..40ed640cd517e1588d1f9a57799bbc257d839c0f 100644 (file)
--- a/krylov_multi_reviewed.tex
+++ b/krylov_multi_reviewed.tex
@@ -354,7 +354,7 @@ We have performed some experiments on an infiniband cluster of three Intel Xeon
 \begin{figure}[htbp]
 \centering
   \includegraphics[width=0.8\textwidth]{strong_scaling_150x150x150}
 \begin{figure}[htbp]
 \centering
   \includegraphics[width=0.8\textwidth]{strong_scaling_150x150x150}

-\caption{Strong scaling with 3 clusters of 4 cores each to solve a 3D Poisson problem of size $150^3$ components}
+\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}
 
 \label{fig:001}
 \end{figure}
 


@@ -363,11 +363,12 @@ We have performed some experiments on an infiniband cluster of three Intel Xeon
 \begin{tabular}{c}
 \includegraphics[width=0.8\textwidth]{weak_scaling_280k} \\ \includegraphics[width=0.8\textwidth]{weak_scaling_280K}\\
 \end{tabular}
 \begin{tabular}{c}
 \includegraphics[width=0.8\textwidth]{weak_scaling_280k} \\ \includegraphics[width=0.8\textwidth]{weak_scaling_280K}\\
 \end{tabular}

-\caption{Weak scaling with 3 clusters of 4 cores each to solve a 3D Poisson problem with approximately 280K components per core}
+\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}
 
 \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 about 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.
+%%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 about 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.

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