Fast and high accuracy multigrid solution of the three dimensional Poisson equation
type: Item
instance of: scholarly article
title: Fast and high accuracy multigrid solution of the three dimensional Poisson equation
zbMATH Open document ID: 0927.65141
author: Jun Zhang
published in: Journal of Computational Physics
publication date: 1999-11-25T00:00:00Z
review text: Multigrid methods for solving the Poisson equation in three-dimensional domains are studied. For the discretization a fourth-order compact difference scheme (19-point scheme) and the usual second-order central difference scheme (7-point scheme) are considered. Using a Fourier analysis it is shown that the smoothing factor of the lexicographic Gauss-Seidel method is smaller in the case of the 19-point scheme than in the case of the 7-point scheme. Furthermore, a new method of Fourier smoothing analysis to study a partially decoupled red-black Gauss-Seidel relaxation with the 19-point scheme is proposed. This analysis shows that the smoothing factor of the red-black Gauss-Seidel smoother is smaller than that of the lexicographic Gauss-Seidel method. The numerical experiments presented confirm these theoretical results. The influence of several grid transfer operators on the convergence behaviour and the efficiency of the multigrid method is studied by numerical experiments.
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 1282711
zbMATH Keywords: Poisson equation
zbMATH Keywords: finite difference method
zbMATH Keywords: multigrid method
zbMATH Keywords: Fourier analysis
zbMATH Keywords: smoothing properties
zbMATH Keywords: numerical examples
zbMATH Keywords: lexicographic Gauss-Seidel method
zbMATH Keywords: red-black Gauss-Seidel relaxation
zbMATH Keywords: convergence
zbMATH Keywords: three-dimensional domains
reviewed by: Michael Jung
describes a project that uses: Wesseling
MaRDI profile type: Publication
OpenAlex ID: W2092707404
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DOI: 10.1006/JCPH.1998.5982
description: scientific article; zbMATH DE number 1282711