The accurate solution of poisson's equation by expansion in chebyshev polynomials

Dale B. Haidvogel; Thomas Zang

doi:10.1016/0021-9991(79)90097-4

The accurate solution of poisson's equation by expansion in chebyshev polynomials

Dale B. Haidvogel, Thomas Zang

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

225 Scopus citations

Abstract

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways-by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

Original language	English (US)
Pages (from-to)	167-180
Number of pages	14
Journal	Journal of Computational Physics
Volume	30
Issue number	2
DOIs	https://doi.org/10.1016/0021-9991(79)90097-4
State	Published - Feb 1979
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

Access to Document

10.1016/0021-9991(79)90097-4

Cite this

@article{d2a8dbc149dd4ca39b288beba78aa6e2,

title = "The accurate solution of poisson's equation by expansion in chebyshev polynomials",

abstract = "A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways-by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.",

author = "Haidvogel, {Dale B.} and Thomas Zang",

note = "Funding Information: The authorsa re gratefult o ProfessorS tevenO rszagf or suggestintgh is approacht o Poisson{\textquoteright}s equationa nd for his advicet hroughoutth is work.S omeo f thec omputetri mew asp rovidedb y the NationalC enterf or AtmospheriRce searchw, hichi s supportebdy theN ationalS cienceF oundation. The work performedby the first authorw ass upportedb y the NationalS cienceF oundationu nder ContractN umberI D076-00869T.h e seconda uthorw as supportedb y NASA ContractN umber NASAl-14101w hile in residencaet ICASE.",

year = "1979",

month = feb,

doi = "10.1016/0021-9991(79)90097-4",

language = "English (US)",

volume = "30",

pages = "167--180",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - The accurate solution of poisson's equation by expansion in chebyshev polynomials

AU - Haidvogel, Dale B.

AU - Zang, Thomas

N1 - Funding Information: The authorsa re gratefult o ProfessorS tevenO rszagf or suggestintgh is approacht o Poisson’s equationa nd for his advicet hroughoutth is work.S omeo f thec omputetri mew asp rovidedb y the NationalC enterf or AtmospheriRce searchw, hichi s supportebdy theN ationalS cienceF oundation. The work performedby the first authorw ass upportedb y the NationalS cienceF oundationu nder ContractN umberI D076-00869T.h e seconda uthorw as supportedb y NASA ContractN umber NASAl-14101w hile in residencaet ICASE.

PY - 1979/2

Y1 - 1979/2

N2 - A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways-by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

AB - A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways-by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

UR - http://www.scopus.com/inward/record.url?scp=49249143705&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49249143705&partnerID=8YFLogxK

U2 - 10.1016/0021-9991(79)90097-4

DO - 10.1016/0021-9991(79)90097-4

M3 - Article

AN - SCOPUS:49249143705

SN - 0021-9991

VL - 30

SP - 167

EP - 180

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -

The accurate solution of poisson's equation by expansion in chebyshev polynomials

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this