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The convergence rate and parallel performance of a 3D elliptic solver

Lirkov I., Vutov V.

Systems Science

2006

Vol. 32, no 4

73-81

It was 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. In this paper, the convergence rate and the parallel performance of a circulant block-factorization based preconditioner applied to a 3D problem are analyzed. A portable parallel code is developed based on Message Passing Interface (MPI) standards. The numerical tests performed on parallel computer systems demonstrate the level of efficiency of the algorithm developed.