Multigrid Method and Fourth Order Compact Difference Scheme
for 2D Poisson Equation with Unequal Meshsize Discretization

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Abstract

A fourth order compact difference scheme with unequal meshsizes in different coordinate directions is employed to discretize 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 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.

Key words: Poisson equation, fourth order compact scheme, unequal meshsize, multigrid method, semicoarsening.

Mathematics Subject Classification: 65M06, 65N12.

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This paper has been published in Journal of Computational Physics, Vol. 179, pp. 170-179 (2002).

Technical Report 321-01, Department of Computer Science, University of Kentucky, Lexington, KY, 2001. This research was supported in part by the U.S. National Science Foundation through a Faculty Early Career Award, and under other NSF grants CCR-9902022, CCR-9988165, and CCR-0092532.