The convergence rate and parallel performance of a 3D elliptic solver
Ivan Lirkov, Vassil Vutov · Systems Science · 2006
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 performed numerical tests on parallel computer systems demonstrate the level of efficiency of the developed algorithm.