From: lilia Date: Thu, 11 Dec 2014 14:16:18 +0000 (+0100) Subject: 11-12-2014 v05 X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Krylov_multi.git/commitdiff_plain/70356990f2020b7ab1a63da30cce096cd34209d6?ds=inline;hp=22203a7ac6e2f98336a298e1c875f1b0580f5769 11-12-2014 v05 --- diff --git a/krylov_multi_reviewed.tex b/krylov_multi_reviewed.tex index 978a03a..a5c7827 100644 --- 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 -process can drastically improve the convergence. +process can drastically improve the convergence.\\ %%% AJOUTE************************ %%%******************************* -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.\\ %%%******************************* %%%******************************* @@ -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} -\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} -\label{fig:001} +\label{fig:002} \end{figure} %%%******************************** diff --git a/strong_scaling_150x150x150.pdf b/strong_scaling_150x150x150.pdf index 8925ec5..b1617b6 100644 Binary files a/strong_scaling_150x150x150.pdf and b/strong_scaling_150x150x150.pdf differ diff --git a/weak_scaling_280K.pdf b/weak_scaling_280K.pdf index a397491..cc94ccd 100644 Binary files a/weak_scaling_280K.pdf and b/weak_scaling_280K.pdf differ diff --git a/weak_scaling_280k.pdf b/weak_scaling_280k.pdf index a918356..376f44d 100644 Binary files a/weak_scaling_280k.pdf and b/weak_scaling_280k.pdf differ