Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation

Yin Wang, Jun Zhang

Research output: Contribution to journalArticlepeer-review

93 Scopus citations

Abstract

We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun-Zhang's sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method.

Original languageEnglish
Pages (from-to)137-146
Number of pages10
JournalJournal of Computational Physics
Volume228
Issue number1
DOIs
StatePublished - Jan 10 2009

Bibliographical note

Funding Information:
This author’s research work was supported in part by NSF under Grants CCF-0727600 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under Grant KSEF-148-502-06-186, in part by the Alzheimer’s Association under Grant NIGR-06-25460, and in part by NIH under Grant 1 R01 HL086644-01.

Keywords

  • Compact difference scheme
  • Multigrid method
  • Poisson equation
  • Richardson extrapolation

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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