Successive overrelaxation, multigrid, and preconditioned conjugate gradients algorithms for solving a diffusion problem on a vector computer

摘要

The purpose of this paper is the treatment of three numerical algorithms [successive overrelaxation (SOR), multigrid (MG) and conjugate gradients preconditioned by a fast Poisson solver (CG)] for solving large but mildly behaved diffusion problems on a vector computer with memory- to-memory architecture. The problem is a symmetric nonnegative definite matrix equation arising from a cell-centered finite difference approximation of a 3-d diffusion equation with full Neumann boundary conditions.