Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative

Michel Fournié; Samir Karaa

doi:10.1007/BF02832060

Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative

Michel Fournié, Samir Karaa^*

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

We derive a fourth-order compact finite difference scheme for a two-dimensional elliptic problem with a mixed derivative and constant coefficients. We conduct experimental study on numerical solution of the problem discretized by the present compact scheme and the traditional second-order central difference scheme. We study the computed accuracy achieved by each scheme and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from the difference schemes.

Original language	English
Pages (from-to)	349-363
Number of pages	15
Journal	Journal of Applied Mathematics and Computing
Volume	22
Issue number	3
DOIs	https://doi.org/10.1007/BF02832060
Publication status	Published - Oct 2006
Externally published	Yes

Keywords

Elliptic problems
compact scheme
iterative methods
mixed derivatives
multigrid method
preconditioning techniques

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/BF02832060

Cite this

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title = "Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative",

abstract = "We derive a fourth-order compact finite difference scheme for a two-dimensional elliptic problem with a mixed derivative and constant coefficients. We conduct experimental study on numerical solution of the problem discretized by the present compact scheme and the traditional second-order central difference scheme. We study the computed accuracy achieved by each scheme and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from the difference schemes.",

keywords = "Elliptic problems, compact scheme, iterative methods, mixed derivatives, multigrid method, preconditioning techniques",

author = "Michel Fourni{\'e} and Samir Karaa",

note = "Funding Information: Received June 27, 2005. Revised N vember 30, 2005. ∗Corresponding author . ∗This author{\textquoteright}s r sear h aw s supported by Sultan Qaboos Univer ity under G nt IG/SCI/ DO-MAS/05/10 {\textcopyright} c 2006 Korean Society for Computational & Applied Mathematics and Korean SIGCAM 349",

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doi = "10.1007/BF02832060",

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T1 - Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative

AU - Fournié, Michel

AU - Karaa, Samir

N1 - Funding Information: Received June 27, 2005. Revised N vember 30, 2005. ∗Corresponding author . ∗This author’s r sear h aw s supported by Sultan Qaboos Univer ity under G nt IG/SCI/ DO-MAS/05/10 © c 2006 Korean Society for Computational & Applied Mathematics and Korean SIGCAM 349

PY - 2006/10

Y1 - 2006/10

N2 - We derive a fourth-order compact finite difference scheme for a two-dimensional elliptic problem with a mixed derivative and constant coefficients. We conduct experimental study on numerical solution of the problem discretized by the present compact scheme and the traditional second-order central difference scheme. We study the computed accuracy achieved by each scheme and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from the difference schemes.

AB - We derive a fourth-order compact finite difference scheme for a two-dimensional elliptic problem with a mixed derivative and constant coefficients. We conduct experimental study on numerical solution of the problem discretized by the present compact scheme and the traditional second-order central difference scheme. We study the computed accuracy achieved by each scheme and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from the difference schemes.

KW - Elliptic problems

KW - compact scheme

KW - iterative methods

KW - mixed derivatives

KW - multigrid method

KW - preconditioning techniques

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DO - 10.1007/BF02832060

M3 - Article

AN - SCOPUS:84867999862

VL - 22

SP - 349

EP - 363

JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

SN - 1598-5865

IS - 3

ER -

Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative

Abstract

Keywords

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