Multigrid method and fourth-order compact scheme for 2D Poisson equation with unequal mesh-size discretization

Jun Zhang

doi:10.1006/jcph.2002.7049

Multigrid method and fourth-order compact scheme for 2D Poisson equation with unequal mesh-size discretization

Jun Zhang

Computer Science

Producción científica: Article › revisión exhaustiva

97 Citas (Scopus)

Resumen

A fourth-order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two-dimensional Poisson equation in a rectangular domain. Multigrid methods using a partial semicoarsening strategy and line Gauss-Seidel relaxation are designed to solve the resulting sparse linear systems. Numerical experiments are conducted to test the accuracy of the fourth-order compact difference scheme and to compare it with the standard second-order difference scheme. Convergence behavior of the partial semicoarsening and line Gauss-Seidel relaxation multigrid methods is examined experimentally.

Idioma original	English
Páginas (desde-hasta)	170-179
Número de páginas	10
Publicación	Journal of Computational Physics
Volumen	179
N.º	1
DOI	https://doi.org/10.1006/jcph.2002.7049
Estado	Published - jun 10 2002

Nota bibliográfica

Funding Information:
1This research was supported by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0092532. 2URL: http://www.cs.uky.edu/∼jzhang.

Financiación

1This research was supported by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0092532. 2URL: http://www.cs.uky.edu/∼jzhang.

Financiadores	Número del financiador
U.S. National Science Foundation (NSF)	CCR-0092532, CCR-9902022, CCR-9988165

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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title = "Multigrid method and fourth-order compact scheme for 2D Poisson equation with unequal mesh-size discretization",

abstract = "A fourth-order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two-dimensional Poisson equation in a rectangular domain. Multigrid methods using a partial semicoarsening strategy and line Gauss-Seidel relaxation are designed to solve the resulting sparse linear systems. Numerical experiments are conducted to test the accuracy of the fourth-order compact difference scheme and to compare it with the standard second-order difference scheme. Convergence behavior of the partial semicoarsening and line Gauss-Seidel relaxation multigrid methods is examined experimentally.",

keywords = "Fourth-order compact scheme, Multigrid method, Poisson equation, Unequal mesh size",

author = "Jun Zhang",

note = "Funding Information: 1This research was supported by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0092532. 2URL: http://www.cs.uky.edu/∼jzhang.",

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Y1 - 2002/6/10

N2 - A fourth-order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two-dimensional Poisson equation in a rectangular domain. Multigrid methods using a partial semicoarsening strategy and line Gauss-Seidel relaxation are designed to solve the resulting sparse linear systems. Numerical experiments are conducted to test the accuracy of the fourth-order compact difference scheme and to compare it with the standard second-order difference scheme. Convergence behavior of the partial semicoarsening and line Gauss-Seidel relaxation multigrid methods is examined experimentally.

AB - A fourth-order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two-dimensional Poisson equation in a rectangular domain. Multigrid methods using a partial semicoarsening strategy and line Gauss-Seidel relaxation are designed to solve the resulting sparse linear systems. Numerical experiments are conducted to test the accuracy of the fourth-order compact difference scheme and to compare it with the standard second-order difference scheme. Convergence behavior of the partial semicoarsening and line Gauss-Seidel relaxation multigrid methods is examined experimentally.

KW - Fourth-order compact scheme

KW - Multigrid method

KW - Poisson equation

KW - Unequal mesh size

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DO - 10.1006/jcph.2002.7049

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SN - 0021-9991

VL - 179

SP - 170

EP - 179

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

Multigrid method and fourth-order compact scheme for 2D Poisson equation with unequal mesh-size discretization

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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