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

Authors:
William M. Cheung;Michael K. Ng
Affiliations:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China;Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

Citing 9
Cited 1

A proposal for toeplitz matrix calculations

Studies in Applied Mathematics
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
The design and analysis of parallel algorithms

The design and analysis of parallel algorithms
Line iterative methods for cyclically reduced discrete convection-diffusion problems

SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Conjugate Gradient Methods for Toeplitz Systems

SIAM Review
Iterative Solution of Cyclically Reduced Systems Arising from Discretization of the Three-Dimensional Convection-Diffusion Equation

SIAM Journal on Scientific Computing
Block Stationary Methods for Nonsymmetric Cyclically Reduced Systems Arising from Three-Dimensional Elliptic Equations

SIAM Journal on Matrix Analysis and Applications
Reduced Systems for Three-Dimensional Elliptic Equations with Variable Coefficients

SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems

On block-circulant preconditioners for high-order compact approximations of convection-diffusion problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

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.