Block-circulant preconditioners for systems arising from discretization of the three-dimensional convection-diffusion equation

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7 Citations (Scopus)

Abstract

We consider the system of equations arising from finite difference discretization of a three-dimensional convection-diffusion model problem. This system is typically nonsymmetric. The GMRES method with the Strang block-circulant preconditioner is proposed for solving this linear system. We show that our preconditioners are invertible and study the spectra of the preconditioned matrices. Numerical results are reported to illustrate the effectiveness of our methods.

Original languageEnglish
Pages (from-to)143-158
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume140
Issue number1-2
DOIs
Publication statusPublished - 2002 Mar 1
Externally publishedYes

Fingerprint

Convection-diffusion Equation
Preconditioner
Linear systems
Discretization
GMRES Method
Three-dimensional
Convection-diffusion
Diffusion Model
Invertible
System of equations
Finite Difference
Strings
Linear Systems
Numerical Results
Convection

Keywords

  • Circulant preconditioner
  • Convection-diffusion equations
  • Finite difference discretization
  • GMRES

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "We consider the system of equations arising from finite difference discretization of a three-dimensional convection-diffusion model problem. This system is typically nonsymmetric. The GMRES method with the Strang block-circulant preconditioner is proposed for solving this linear system. We show that our preconditioners are invertible and study the spectra of the preconditioned matrices. Numerical results are reported to illustrate the effectiveness of our methods.",
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AU - Cheung, Ming Yan William

AU - Ng, Michael K.

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N2 - We consider the system of equations arising from finite difference discretization of a three-dimensional convection-diffusion model problem. This system is typically nonsymmetric. The GMRES method with the Strang block-circulant preconditioner is proposed for solving this linear system. We show that our preconditioners are invertible and study the spectra of the preconditioned matrices. Numerical results are reported to illustrate the effectiveness of our methods.

AB - We consider the system of equations arising from finite difference discretization of a three-dimensional convection-diffusion model problem. This system is typically nonsymmetric. The GMRES method with the Strang block-circulant preconditioner is proposed for solving this linear system. We show that our preconditioners are invertible and study the spectra of the preconditioned matrices. Numerical results are reported to illustrate the effectiveness of our methods.

KW - Circulant preconditioner

KW - Convection-diffusion equations

KW - Finite difference discretization

KW - GMRES

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