From: lilia Date: Wed, 30 Apr 2014 16:00:46 +0000 (+0200) Subject: v2 X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Krylov_multi.git/commitdiff_plain/6d8fffd4d9fc58efe4a9ff5d7cd81767782ba572 v2 --- diff --git a/krylov_multi.tex b/krylov_multi.tex index 2d0bc69..87ee227 100644 --- a/krylov_multi.tex +++ b/krylov_multi.tex @@ -67,15 +67,17 @@ Preconditioners can be used in order to increase the convergence of iterative solvers. However, most of the good preconditioners are not scalable when thousands of cores are used. -Traditional iterative solvers have global synchronizations that penalize the -scalability. Two possible solutions consists either in using asynchronous -iterative methods~\cite{ref18} or to use multisplitting algorithms. 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. - -The paper is organized as follows. First in Section~\ref{sec:02} is given some related works and the main principle of multisplitting methods. The, in Section~\ref{sec:03} is presented the algorithm of our Krylov multisplitting method based on inner-outer iterations. Finally, in Section~\ref{sec:04}, the parallel experiments on Hector architecture show the performances of the Krylov multisplitting algorithm compared to the classical GMRES algorithm to solve a 3D Poisson problem. +%Traditional iterative solvers have global synchronizations that penalize the +%scalability. Two possible solutions consists either in using asynchronous +%iterative methods~\cite{ref18} or to use multisplitting algorithms. 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. + +Traditional parallel iterative solvers are based on fine-grain computations that frequently require data exchanges between computing nodes and have global synchronizations that penalize the scalability. Particularly, they are more penalized on large scale architectures or on distributed platforms composed of distant clusters interconnected by a high-latency network. It is therefore imperative to develop coarse-grain based algorithms to reduce the communications in the parallel iterative solvers. Two possible solutions consists either in using asynchronous iterative methods~\cite{ref18} or to use multisplitting algorithms. 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. + +The present paper is organized as follows. First in Section~\ref{sec:02} is given some related works and the main principle of multisplitting methods. Then, in Section~\ref{sec:03} is presented the algorithm of our Krylov multisplitting method based on inner-outer iterations. Finally, in Section~\ref{sec:04}, the parallel experiments on Hector architecture show the performances of the Krylov multisplitting algorithm compared to the classical GMRES algorithm to solve a 3D Poisson problem. %%%%%%%%%%%%%%%%%%%%%%%%