Preconditioned iterative methods and finite difference schemes for convection-diffusion

Jun Zhang

doi:10.1016/S0096-3003(99)00013-2

Preconditioned iterative methods and finite difference schemes for convection-diffusion

Jun Zhang

Computer Science

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

We conduct experimental study on numerical solution of the two dimensional convection-diffusion equation discretized by three finite difference schemes: the traditional central difference scheme, the standard upwind scheme and the fourth-order compact scheme. We study the computed accuracy achievable by each scheme, the algebraic properties of the coefficient matrices arising from different schemes and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from these schemes.

Original language	English
Pages (from-to)	11-30
Number of pages	20
Journal	Applied Mathematics and Computation
Volume	109
Issue number	1
DOIs	https://doi.org/10.1016/S0096-3003(99)00013-2
State	Published - Mar 1 2000

Keywords

Convection-diffusion equation
Finite difference discretization
Iterative methods
Preconditioning techniques

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0096-3003(99)00013-2

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abstract = "We conduct experimental study on numerical solution of the two dimensional convection-diffusion equation discretized by three finite difference schemes: the traditional central difference scheme, the standard upwind scheme and the fourth-order compact scheme. We study the computed accuracy achievable by each scheme, the algebraic properties of the coefficient matrices arising from different schemes and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from these schemes.",

keywords = "Convection-diffusion equation, Finite difference discretization, Iterative methods, Preconditioning techniques",

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N2 - We conduct experimental study on numerical solution of the two dimensional convection-diffusion equation discretized by three finite difference schemes: the traditional central difference scheme, the standard upwind scheme and the fourth-order compact scheme. We study the computed accuracy achievable by each scheme, the algebraic properties of the coefficient matrices arising from different schemes and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from these schemes.

AB - We conduct experimental study on numerical solution of the two dimensional convection-diffusion equation discretized by three finite difference schemes: the traditional central difference scheme, the standard upwind scheme and the fourth-order compact scheme. We study the computed accuracy achievable by each scheme, the algebraic properties of the coefficient matrices arising from different schemes and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from these schemes.

KW - Convection-diffusion equation

KW - Finite difference discretization

KW - Iterative methods

KW - Preconditioning techniques

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EP - 30

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

Preconditioned iterative methods and finite difference schemes for convection-diffusion

Abstract

Keywords

ASJC Scopus subject areas

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