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

Jun Zhang

Research output: Contribution to journalArticlepeer-review

94 Scopus citations

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.

Original languageEnglish
Pages (from-to)170-179
Number of pages10
JournalJournal of Computational Physics
Volume179
Issue number1
DOIs
StatePublished - Jun 10 2002

Bibliographical 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.

Keywords

  • Fourth-order compact scheme
  • Multigrid method
  • Poisson equation
  • Unequal mesh size

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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