Parallel performance of a 3d elliptic solver

Authors:
Ivan Lirkov
Affiliations:
Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria
Venue:
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Year:
2004

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Circulant block-factorization preconditioning of anisotropic elliptic problems

Computing
MPI: The Complete Reference

MPI: The Complete Reference

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Abstract

It was recently shown that block-circulant preconditioners applied to a conjugate gradient method used to solve structured sparse linear systems arising from 2D or 3D elliptic problems have good numerical properties and a potential for high parallel efficiency. The asymptotic estimate for their convergence rate is as for the incomplete factorization methods but the efficiency of the parallel algorithms based on circulant preconditioners are asymptotically optimal. In this paper parallel performance of a circulant block-factorization based preconditioner applied to a 3D model problem is investigated. The aim of this presentation is to analyze the performance and to report on the experimental results obtained on shared and distributed memory parallel architectures. A portable parallel code is developed based on Message Passing Interface (MPI) and OpenMP (Open Multi Processing) standards. The performed numerical tests on a wide range of parallel computer systems clearly demonstrate the high level of parallel efficiency of the developed parallel code.