A novel multigrid based preconditioner for heterogeneous Helmholtz problems

Y. A. Erlangga; C. W. Oosterlee; C. Vuik

doi:10.1137/040615195

A novel multigrid based preconditioner for heterogeneous Helmholtz problems

Y. A. Erlangga^*, C. W. Oosterlee, C. Vuik

^*Corresponding author for this work

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

Abstract

An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wavenumber Helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner.

Original language	English
Pages (from-to)	1471-1492
Number of pages	22
Journal	SIAM Journal on Scientific Computing
Volume	27
Issue number	4
DOIs	https://doi.org/10.1137/040615195
Publication status	Published - 2006
Externally published	Yes

Keywords

Complex multigrid preconditioner
Fourier analysis
Helmholtz equation
Nonconstant high wavenumber

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10.1137/040615195

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title = "A novel multigrid based preconditioner for heterogeneous Helmholtz problems",

abstract = "An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wavenumber Helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner.",

keywords = "Complex multigrid preconditioner, Fourier analysis, Helmholtz equation, Nonconstant high wavenumber",

author = "Erlangga, {Y. A.} and Oosterlee, {C. W.} and C. Vuik",

year = "2006",

doi = "10.1137/040615195",

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journal = "SIAM Journal on Scientific Computing",

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AU - Erlangga, Y. A.

AU - Oosterlee, C. W.

AU - Vuik, C.

PY - 2006

Y1 - 2006

N2 - An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wavenumber Helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner.

AB - An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wavenumber Helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner.

KW - Complex multigrid preconditioner

KW - Fourier analysis

KW - Helmholtz equation

KW - Nonconstant high wavenumber

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EP - 1492

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 4

ER -

A novel multigrid based preconditioner for heterogeneous Helmholtz problems

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Keywords

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