A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation

Jun Zhang; Lixin Ge; Jules Kouatchou

doi:10.1016/s0378-4754(00)00205-6

A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation

Jun Zhang
, Lixin Ge
, Jules Kouatchou

Computer Science

Producción científica: Article › revisión exhaustiva

46 Citas (Scopus)

Resumen

A new fourth-order compact difference scheme for the three-dimensional (3D) convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with a Gauss-Seidel type iterative method. This is compared with the known 19-point fourth-order compact difference scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15- and 19-point fourth-order compact schemes.

Idioma original	English
Páginas (desde-hasta)	65-80
Número de páginas	16
Publicación	Mathematics and Computers in Simulation
Volumen	54
N.º	1-3
DOI	https://doi.org/10.1016/s0378-4754(00)00205-6
Estado	Published - nov 30 2000

Nota bibliográfica

Funding Information:
The research of the author Jun Zhang was supported in part by the US National Science Foundation under the Grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences. The research of the author Lixin Ge was supported by the University of Kentucky Center for Computational Sciences. The author Jules Kouatchou is affiliated with Morgan State University and his research was supported by NASA under the Grant no. NAGS-3508.

Financiación

The research of the author Jun Zhang was supported in part by the US National Science Foundation under the Grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences. The research of the author Lixin Ge was supported by the University of Kentucky Center for Computational Sciences. The author Jules Kouatchou is affiliated with Morgan State University and his research was supported by NASA under the Grant no. NAGS-3508.

Financiadores	Número del financiador
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	CCR-9902022
National Aeronautics and Space Administration	NAGS-3508
University of Kentucky Information Technology Department and Center for Computational Sciences

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Numerical Analysis
Modeling and Simulation
Applied Mathematics

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title = "A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation",

abstract = "A new fourth-order compact difference scheme for the three-dimensional (3D) convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with a Gauss-Seidel type iterative method. This is compared with the known 19-point fourth-order compact difference scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15- and 19-point fourth-order compact schemes.",

keywords = "3D convection diffusion equation, Fourth-order compact difference schemes, Multigrid method, Parallel computation",

author = "Jun Zhang and Lixin Ge and Jules Kouatchou",

note = "Funding Information: The research of the author Jun Zhang was supported in part by the US National Science Foundation under the Grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences. The research of the author Lixin Ge was supported by the University of Kentucky Center for Computational Sciences. The author Jules Kouatchou is affiliated with Morgan State University and his research was supported by NASA under the Grant no. NAGS-3508. ",

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T1 - A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation

AU - Zhang, Jun

AU - Ge, Lixin

AU - Kouatchou, Jules

N1 - Funding Information: The research of the author Jun Zhang was supported in part by the US National Science Foundation under the Grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences. The research of the author Lixin Ge was supported by the University of Kentucky Center for Computational Sciences. The author Jules Kouatchou is affiliated with Morgan State University and his research was supported by NASA under the Grant no. NAGS-3508.

PY - 2000/11/30

Y1 - 2000/11/30

N2 - A new fourth-order compact difference scheme for the three-dimensional (3D) convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with a Gauss-Seidel type iterative method. This is compared with the known 19-point fourth-order compact difference scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15- and 19-point fourth-order compact schemes.

AB - A new fourth-order compact difference scheme for the three-dimensional (3D) convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with a Gauss-Seidel type iterative method. This is compared with the known 19-point fourth-order compact difference scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15- and 19-point fourth-order compact schemes.

KW - 3D convection diffusion equation

KW - Fourth-order compact difference schemes

KW - Multigrid method

KW - Parallel computation

UR - https://www.scopus.com/pages/publications/0010975108

UR - https://www.scopus.com/pages/publications/0010975108#tab=citedBy

U2 - 10.1016/s0378-4754(00)00205-6

DO - 10.1016/s0378-4754(00)00205-6

M3 - Article

AN - SCOPUS:0010975108

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VL - 54

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JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

IS - 1-3

ER -

A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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