Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation

Yin Wang; Jun Zhang

doi:10.1016/j.jcp.2008.09.002

Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation

Yin Wang
, Jun Zhang

Computer Science

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

100 Scopus citations

Abstract

We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun-Zhang's sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method.

Original language	English
Pages (from-to)	137-146
Number of pages	10
Journal	Journal of Computational Physics
Volume	228
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2008.09.002
State	Published - Jan 10 2009

Bibliographical note

Funding Information:
This author’s research work was supported in part by NSF under Grants CCF-0727600 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under Grant KSEF-148-502-06-186, in part by the Alzheimer’s Association under Grant NIGR-06-25460, and in part by NIH under Grant 1 R01 HL086644-01.

Funding

This author’s research work was supported in part by NSF under Grants CCF-0727600 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under Grant KSEF-148-502-06-186, in part by the Alzheimer’s Association under Grant NIGR-06-25460, and in part by NIH under Grant 1 R01 HL086644-01.

Funders	Funder number
Kentucky Science and Engineering Foundation	KSEF-148-502-06-186
Kentucky Science and Engineering Foundation
National Science Foundation Arctic Social Science Program	CCF-0527967, CCF-0727600
National Science Foundation Arctic Social Science Program
National Institutes of Health (NIH)	1 R01 HL086644-01
National Institutes of Health (NIH)
Alzheimer's Association	NIGR-06-25460
Alzheimer's Association

Keywords

Compact difference scheme
Multigrid method
Poisson equation
Richardson extrapolation

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2008.09.002

Cite this

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title = "Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation",

abstract = "We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun-Zhang's sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method.",

keywords = "Compact difference scheme, Multigrid method, Poisson equation, Richardson extrapolation",

author = "Yin Wang and Jun Zhang",

note = "Funding Information: This author{\textquoteright}s research work was supported in part by NSF under Grants CCF-0727600 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under Grant KSEF-148-502-06-186, in part by the Alzheimer{\textquoteright}s Association under Grant NIGR-06-25460, and in part by NIH under Grant 1 R01 HL086644-01. ",

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AU - Wang, Yin

AU - Zhang, Jun

N1 - Funding Information: This author’s research work was supported in part by NSF under Grants CCF-0727600 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under Grant KSEF-148-502-06-186, in part by the Alzheimer’s Association under Grant NIGR-06-25460, and in part by NIH under Grant 1 R01 HL086644-01.

PY - 2009/1/10

Y1 - 2009/1/10

N2 - We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun-Zhang's sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method.

AB - We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun-Zhang's sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method.

KW - Compact difference scheme

KW - Multigrid method

KW - Poisson equation

KW - Richardson extrapolation

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SN - 0021-9991

VL - 228

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JO - Journal of Computational Physics

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ER -

Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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