A general meshsize fourth-order compact difference discretization scheme for 3D Poisson equation

Jie Wang, Weijun Zhong, Jun Zhang

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

A fourth-order compact difference scheme with unrestricted general meshsizes in different coordinate directions is derived to discretize three-dimensional Poisson equation on a regular cubic domain. The difference scheme derivation procedure makes use of the symbolic representation of the finite difference schemes and is easier to understand in such complex three-dimensional manipulations. We use a preconditioned conjugate gradient method to solve the resulting sparse linear systems and verify the formal order of convergence of the derived fourth-order finite difference scheme.

Original languageEnglish
Pages (from-to)804-812
Number of pages9
JournalApplied Mathematics and Computation
Volume183
Issue number2
DOIs
StatePublished - Dec 15 2006

Keywords

  • Fourth-order compact scheme
  • General meshsize
  • Iterative methods
  • Poisson equation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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