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

Jie Wang; Weijun Zhong; Jun Zhang

doi:10.1016/j.amc.2006.06.028

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

Jie Wang, Weijun Zhong, Jun Zhang

Computer Science

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	804-812
Number of pages	9
Journal	Applied Mathematics and Computation
Volume	183
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2006.06.028
State	Published - 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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10.1016/j.amc.2006.06.028

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title = "A general meshsize fourth-order compact difference discretization scheme for 3D Poisson equation",

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.",

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AU - Wang, Jie

AU - Zhong, Weijun

AU - Zhang, Jun

PY - 2006/12/15

Y1 - 2006/12/15

N2 - 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.

AB - 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.

KW - Fourth-order compact scheme

KW - General meshsize

KW - Iterative methods

KW - Poisson equation

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SP - 804

EP - 812

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

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

Abstract

Keywords

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