11-12-2014 v05

[Krylov_multi.git] / krylov_multi_reviewed.tex

diff --git a/krylov_multi_reviewed.tex b/krylov_multi_reviewed.tex
index 978a03a86e2ca3981f1c3fbbb27de7c5d23aa765..a5c7827164382f23aa4c32b953e0db3249ff9a3b 100644 (file)
--- a/krylov_multi_reviewed.tex
+++ b/krylov_multi_reviewed.tex
@@ -93,12 +93,13 @@ using  asynchronous  iterative  methods~\cite{ref18}  or in  using  multisplitti
 algorithmss.  In this  paper,  we will  reconsider  the use  of a  multisplitting
 method. In opposition to traditional multisplitting method that suffer from slow
 convergence, as  proposed in~\cite{huang1993krylov},  the use of  a minimization
 algorithmss.  In this  paper,  we will  reconsider  the use  of a  multisplitting
 method. In opposition to traditional multisplitting method that suffer from slow
 convergence, as  proposed in~\cite{huang1993krylov},  the use of  a minimization

-process can drastically improve the convergence.
+process can drastically improve the convergence.\\

 
 
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-In this work we develop a new parallel two-stage algorithm for large-scale clusters. Our objective is to mix between Krylov based iterative methods and the multisplitting method to improve the scalability. In fact Krylov subspace methods are well-known for their good convergence compared to others iterative methods. So our main contribution is to use the multisplitting method which splits the problem to solve into different blocks in order to reduce the large amount of communications and, to implement both inner and outer iterations as Krylov subspace iterations improving the convergence of the multisplitting algorithm.
+\noindent {\bf Contributions:}\\ 
+In this work we develop a new parallel two-stage algorithm for large-scale clusters. Our objective is to mix between Krylov based iterative methods and the multisplitting method to improve the scalability. In fact Krylov subspace methods are well-known for their good convergence compared to others iterative methods. So our main contribution is to use the multisplitting method which splits the problem to solve into different blocks in order to reduce the large amount of communications and, to implement both inner and outer iterations as Krylov subspace iterations improving the convergence of the multisplitting algorithm.\\

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@@ -359,10 +360,10 @@ We have performed some experiments on an infiniband cluster of 3 nodes of Intel
 \begin{figure}[htbp]
 \centering
 \begin{tabular}{c}
 \begin{figure}[htbp]
 \centering
 \begin{tabular}{c}

-\includegraphics[width=0.8\textwidth]{weak_scaling_280k} \\ (a) \includegraphics[width=0.8\textwidth]{weak_scaling_280K}\\
+\includegraphics[width=0.8\textwidth]{weak_scaling_280k} \\ \includegraphics[width=0.8\textwidth]{weak_scaling_280K}\\

 \end{tabular}
 \caption{Weak scaling with 3 blocks of cores}
 \end{tabular}
 \caption{Weak scaling with 3 blocks of cores}

-\label{fig:001}
+\label{fig:002}

 \end{figure}
 
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 \end{figure}
 
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