DMCA
Fast and High Accuracy Multigrid Solution of the Three Dimensional Poisson Equation (1998)
| Venue: | J. Comput. Phys |
| Citations: | 17 - 7 self |
BibTeX
@ARTICLE{Zhang98fastand,
author = {Jun Zhang},
title = {Fast and High Accuracy Multigrid Solution of the Three Dimensional Poisson Equation},
journal = {J. Comput. Phys},
year = {1998},
volume = {143},
pages = {449--461}
}
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Abstract
We employ a fourth-order compact finite difference scheme (FOS) with the multigrid algorithm to solve the three dimensional Poisson equation. We test the influence of different orderings of the grid space and different grid-transfer operators on the convergence and efficiency of our high accuracy algorithm. Fourier smoothing analysis is conducted to show that FOS has a smaller smoothing factor than the traditional second-order central difference scheme (CDS). A new method of Fourier smoothing analysis is proposed for the partially decoupled red-black Gauss-Seidel relaxation with FOS. Numerical results are given to compare the computed accuracy and the computational efficiency of FOS with multigrid against CDS with multigrid. 1991 Mathematical Subject Classification: 65F10, 65N06, 65N22, 65N55. Key words: Poisson equation, multigrid method, fourth-order compact scheme, Fourier smoothing analysis. 1 Introduction Numerical simulation of three-dimensional (3D) problems tends to be comput...
Keyphrases
three dimensional poisson equation high accuracy multigrid solution computational efficiency multigrid algorithm grid space poisson equation traditional second-order central difference scheme introduction numerical simulation key word different ordering different grid-transfer operator high accuracy algorithm numerical result smoothing factor computed accuracy fourth-order compact finite difference scheme dimensional poisson equation fourth-order compact scheme mathematical subject classification multigrid method decoupled red-black gauss-seidel relaxation new method
