A transformation-free hoc scheme and multigrid method for solving the 3d poisson equation on nonuniform grids

Yongbin Ge; Fujun Cao; Jun Zhang

doi:10.1016/j.jcp.2012.09.034

A transformation-free hoc scheme and multigrid method for solving the 3d poisson equation on nonuniform grids

Yongbin Ge, Fujun Cao, Jun Zhang

Computer Science

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

26 Scopus citations

Abstract

A high-order compact (HOC) difference scheme is proposed to solve the three-dimensional (3D) Poisson equation on nonuniform orthogonal Cartesian grids involving no coordinate transformation from the physical space to the computational space. Theoretically, the proposed scheme has third to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Then, a multigrid method is developed to solve the linear system arising from this HOC difference scheme and the corresponding multigrid restriction and interpolation operators are constructed using the volume law. Numerical experiments are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the multigrid method.

Original language	English
Pages (from-to)	199-216
Number of pages	18
Journal	Journal of Computational Physics
Volume	234
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2012.09.034
State	Published - 2013

Bibliographical note

Funding Information:
This work is supported by the National Natural Science Foundation of China under Grants 11061025 and 11161036 , the Key Project of China Ministry of Education under Grant 210239 , and the Fok Ying-Tong Education Foundation of China under Grant 121105 .

Funding

This work is supported by the National Natural Science Foundation of China under Grants 11061025 and 11161036 , the Key Project of China Ministry of Education under Grant 210239 , and the Fok Ying-Tong Education Foundation of China under Grant 121105 .

Funders	Funder number
National Natural Science Foundation of P.R. China	11061025, 11161036
National Natural Science Foundation of P.R. China
Ministry of Education of the People's Republic of China	210239
Ministry of Education of the People's Republic of China
Fok Ying-Tong Education Foundation	121105
Fok Ying-Tong Education Foundation

Keywords

Hoc scheme
Multigrid method
Nonuniform grids
Poisson equations
Volume law

ASJC Scopus subject areas

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

Access to Document

10.1016/j.jcp.2012.09.034

Cite this

@article{adc67d92e9f24953bb25995ee628e37a,

title = "A transformation-free hoc scheme and multigrid method for solving the 3d poisson equation on nonuniform grids",

abstract = "A high-order compact (HOC) difference scheme is proposed to solve the three-dimensional (3D) Poisson equation on nonuniform orthogonal Cartesian grids involving no coordinate transformation from the physical space to the computational space. Theoretically, the proposed scheme has third to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Then, a multigrid method is developed to solve the linear system arising from this HOC difference scheme and the corresponding multigrid restriction and interpolation operators are constructed using the volume law. Numerical experiments are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the multigrid method.",

keywords = "Hoc scheme, Multigrid method, Nonuniform grids, Poisson equations, Volume law",

author = "Yongbin Ge and Fujun Cao and Jun Zhang",

note = "Funding Information: This work is supported by the National Natural Science Foundation of China under Grants 11061025 and 11161036 , the Key Project of China Ministry of Education under Grant 210239 , and the Fok Ying-Tong Education Foundation of China under Grant 121105 .",

year = "2013",

doi = "10.1016/j.jcp.2012.09.034",

language = "English",

volume = "234",

pages = "199--216",

number = "1",

}

TY - JOUR

T1 - A transformation-free hoc scheme and multigrid method for solving the 3d poisson equation on nonuniform grids

AU - Ge, Yongbin

AU - Cao, Fujun

AU - Zhang, Jun

N1 - Funding Information: This work is supported by the National Natural Science Foundation of China under Grants 11061025 and 11161036 , the Key Project of China Ministry of Education under Grant 210239 , and the Fok Ying-Tong Education Foundation of China under Grant 121105 .

PY - 2013

Y1 - 2013

N2 - A high-order compact (HOC) difference scheme is proposed to solve the three-dimensional (3D) Poisson equation on nonuniform orthogonal Cartesian grids involving no coordinate transformation from the physical space to the computational space. Theoretically, the proposed scheme has third to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Then, a multigrid method is developed to solve the linear system arising from this HOC difference scheme and the corresponding multigrid restriction and interpolation operators are constructed using the volume law. Numerical experiments are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the multigrid method.

AB - A high-order compact (HOC) difference scheme is proposed to solve the three-dimensional (3D) Poisson equation on nonuniform orthogonal Cartesian grids involving no coordinate transformation from the physical space to the computational space. Theoretically, the proposed scheme has third to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Then, a multigrid method is developed to solve the linear system arising from this HOC difference scheme and the corresponding multigrid restriction and interpolation operators are constructed using the volume law. Numerical experiments are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the multigrid method.

KW - Hoc scheme

KW - Multigrid method

KW - Nonuniform grids

KW - Poisson equations

KW - Volume law

UR - https://www.scopus.com/pages/publications/84870562355

UR - https://www.scopus.com/inward/citedby.url?scp=84870562355&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2012.09.034

DO - 10.1016/j.jcp.2012.09.034

M3 - Article

AN - SCOPUS:84870562355

SN - 0021-9991

VL - 234

SP - 199

EP - 216

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

A transformation-free hoc scheme and multigrid method for solving the 3d poisson equation on nonuniform grids

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this