Shifted-laplacian preconditioners for heterogeneous helmholtz problems

C. W. Oosterlee; C. Vuik; W. A. Mulder; R. E. Plessix

doi:10.1007/978-3-642-03344-5_2

Shifted-laplacian preconditioners for heterogeneous helmholtz problems

C. W. Oosterlee^*, C. Vuik, W. A. Mulder, R. E. Plessix

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

We present an iterative solution method for the discrete high wavenumber Helmholtz equation. The basic idea of the solution method, already presented in [18], is to develop a preconditioner which is based on a Helmholtz operator with a complex-valued shift, for a Krylov subspace iterative method. The preconditioner, which can be seen as a strongly damped wave equation in Fourier space, can be approximately inverted by a multigrid method.

Original language	English
Title of host publication	Advanced Computational Methods in Science and Engineering
Publisher	Springer
Pages	21-46
Number of pages	26
ISBN (Print)	9783642033438
DOIs	https://doi.org/10.1007/978-3-642-03344-5_2
Publication status	Published - 2010
Externally published	Yes

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	71
ISSN (Print)	1439-7358

Funding

Acknowledgment The authors would like to thank Shell International Exploration and Production and Philips for their financial support to this BTS project. Furthermore, they would like to thank Y.A. Erlangga, Ch. Dwi Riyanti, A. Kononov, M.B.

Access to Document

10.1007/978-3-642-03344-5_2

Cite this

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title = "Shifted-laplacian preconditioners for heterogeneous helmholtz problems",

abstract = "We present an iterative solution method for the discrete high wavenumber Helmholtz equation. The basic idea of the solution method, already presented in [18], is to develop a preconditioner which is based on a Helmholtz operator with a complex-valued shift, for a Krylov subspace iterative method. The preconditioner, which can be seen as a strongly damped wave equation in Fourier space, can be approximately inverted by a multigrid method.",

author = "Oosterlee, {C. W.} and C. Vuik and Mulder, {W. A.} and Plessix, {R. E.}",

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doi = "10.1007/978-3-642-03344-5_2",

language = "English",

isbn = "9783642033438",

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Shifted-laplacian preconditioners for heterogeneous helmholtz problems. / Oosterlee, C. W.; Vuik, C.; Mulder, W. A. et al.
Advanced Computational Methods in Science and Engineering. Springer, 2010. p. 21-46 (Lecture Notes in Computational Science and Engineering; Vol. 71).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Plessix, R. E.

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N2 - We present an iterative solution method for the discrete high wavenumber Helmholtz equation. The basic idea of the solution method, already presented in [18], is to develop a preconditioner which is based on a Helmholtz operator with a complex-valued shift, for a Krylov subspace iterative method. The preconditioner, which can be seen as a strongly damped wave equation in Fourier space, can be approximately inverted by a multigrid method.

AB - We present an iterative solution method for the discrete high wavenumber Helmholtz equation. The basic idea of the solution method, already presented in [18], is to develop a preconditioner which is based on a Helmholtz operator with a complex-valued shift, for a Krylov subspace iterative method. The preconditioner, which can be seen as a strongly damped wave equation in Fourier space, can be approximately inverted by a multigrid method.

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M3 - Conference contribution

AN - SCOPUS:84941418922

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T3 - Lecture Notes in Computational Science and Engineering

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BT - Advanced Computational Methods in Science and Engineering

PB - Springer

ER -

Shifted-laplacian preconditioners for heterogeneous helmholtz problems

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