A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation

Jun Zhang, Lixin Ge, Jules Kouatchou

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

A new fourth-order compact difference scheme for the three-dimensional (3D) convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with a Gauss-Seidel type iterative method. This is compared with the known 19-point fourth-order compact difference scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15- and 19-point fourth-order compact schemes.

Original languageEnglish
Pages (from-to)65-80
Number of pages16
JournalMathematics and Computers in Simulation
Volume54
Issue number1-3
DOIs
StatePublished - Nov 30 2000

Bibliographical note

Funding Information:
The research of the author Jun Zhang was supported in part by the US National Science Foundation under the Grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences. The research of the author Lixin Ge was supported by the University of Kentucky Center for Computational Sciences. The author Jules Kouatchou is affiliated with Morgan State University and his research was supported by NASA under the Grant no. NAGS-3508.

Keywords

  • 3D convection diffusion equation
  • Fourth-order compact difference schemes
  • Multigrid method
  • Parallel computation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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