Convergence and performance of iterative methods for solving variable coefficient convection-diffusion equation with a fourth-order compact difference scheme

S. Karaa, Jun Zhang

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We conduct convergence analysis on some classical stationary iterative methods for solving the two-dimensional variable coefficient convection-diffusion equation discretized by a fourth-order compact difference scheme. Several conditions are formulated under which the coefficient matrix is guaranteed to be an M-matrix. We further investigate the effect of different orderings of the grid points on the performance of some stationary iterative methods, multigrid method, and preconditioned GMRES. Three sets of numerical experiments are conducted to study the convergence behaviors of these iterative methods under the influence of the flow directions, the orderings of the grid points, and the magnitude of the convection coefficients.

Original languageEnglish
Pages (from-to)457-479
Number of pages23
JournalComputers and Mathematics with Applications
Volume44
Issue number3-4
DOIs
Publication statusPublished - Aug 2002

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Compact Scheme
Convection-diffusion Equation
Iterative methods
Difference Scheme
Variable Coefficients
Fourth Order
Iteration
Grid
GMRES
Multigrid Method
M-matrix
Coefficient
Convergence Analysis
Convection
Numerical Experiment
Experiments

Keywords

  • Convection-diffusion equation
  • Fourth-order compact scheme
  • Grid ordering
  • Iterative methods
  • Multicoloring

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

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AB - We conduct convergence analysis on some classical stationary iterative methods for solving the two-dimensional variable coefficient convection-diffusion equation discretized by a fourth-order compact difference scheme. Several conditions are formulated under which the coefficient matrix is guaranteed to be an M-matrix. We further investigate the effect of different orderings of the grid points on the performance of some stationary iterative methods, multigrid method, and preconditioned GMRES. Three sets of numerical experiments are conducted to study the convergence behaviors of these iterative methods under the influence of the flow directions, the orderings of the grid points, and the magnitude of the convection coefficients.

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