From 70356990f2020b7ab1a63da30cce096cd34209d6 Mon Sep 17 00:00:00 2001 From: lilia Date: Thu, 11 Dec 2014 15:16:18 +0100 Subject: [PATCH 1/1] 11-12-2014 v05 --- krylov_multi_reviewed.tex | 9 +++++---- strong_scaling_150x150x150.pdf | Bin 14432 -> 14442 bytes weak_scaling_280K.pdf | Bin 14368 -> 14453 bytes weak_scaling_280k.pdf | Bin 14464 -> 14523 bytes 4 files changed, 5 insertions(+), 4 deletions(-) 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 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