An iterative method for the Helmholtz equation

Alvin Bayliss; Charles I. Goldstein; Eli Turkel

doi:10.1016/0021-9991(83)90139-0

An iterative method for the Helmholtz equation

Alvin Bayliss^*, Charles I. Goldstein, Eli Turkel

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

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

169 Scopus citations

Abstract

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Original language	English (US)
Pages (from-to)	443-457
Number of pages	15
Journal	Journal of Computational Physics
Volume	49
Issue number	3
DOIs	https://doi.org/10.1016/0021-9991(83)90139-0
State	Published - Mar 1983

ASJC Scopus subject areas

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

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10.1016/0021-9991(83)90139-0

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@article{3e589070b190438380d67c7bb5508648,

title = "An iterative method for the Helmholtz equation",

abstract = "An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.",

author = "Alvin Bayliss and Goldstein, {Charles I.} and Eli Turkel",

note = "Funding Information: * This work was partially supported by the National Aeronautics and Space Administration under Contracts NASl-14472 and NASl-16394 while the first and third authors were in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665. Additional support for the first author was provided by Air Force Contract AFOSR-81-0020 and the U.S. Department of Energy Contract DE-AC02-76ER03077. Research of the second author was supported by Contract DE-AC02-76CHOOO16 with the U.S. Department of Energy.",

year = "1983",

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doi = "10.1016/0021-9991(83)90139-0",

language = "English (US)",

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journal = "Journal of Computational Physics",

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T1 - An iterative method for the Helmholtz equation

AU - Bayliss, Alvin

AU - Goldstein, Charles I.

AU - Turkel, Eli

N1 - Funding Information: * This work was partially supported by the National Aeronautics and Space Administration under Contracts NASl-14472 and NASl-16394 while the first and third authors were in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665. Additional support for the first author was provided by Air Force Contract AFOSR-81-0020 and the U.S. Department of Energy Contract DE-AC02-76ER03077. Research of the second author was supported by Contract DE-AC02-76CHOOO16 with the U.S. Department of Energy.

PY - 1983/3

Y1 - 1983/3

N2 - An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

AB - An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

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An iterative method for the Helmholtz equation

Abstract

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