Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation

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

doi:10.1016/j.apnum.2005.04.039

Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation

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

^*Corresponding author for this work

Delft University of Technology

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

Abstract

Within the framework of shifted-Laplace preconditioners [Y.A. Erlangga, C. Vuik, C.W. Oosterlee, On a class of preconditioners for the Helmholtz equation, Appl. Numer. Math. 50 (2004) 409-425] for the Helmholtz equation, different methods for the approximation of the inverse of a complex-valued Helmholtz operator are discussed. The performance of the preconditioner for Helmholtz problems at high wavenumbers in heterogeneous media is evaluated. Comparison with other preconditioners from the literature is also presented.

Original language	English
Pages (from-to)	648-666
Number of pages	19
Journal	Applied Numerical Mathematics
Volume	56
Issue number	5
DOIs	https://doi.org/10.1016/j.apnum.2005.04.039
Publication status	Published - May 2006
Externally published	Yes

Bibliographical note

Funding Information:
✩ The research is financially supported by the Dutch Ministry of Economic Affairs under the Project BTS01044. E-mail addresses: [email protected] (Y.A. Erlangga), [email protected] (C. Vuik), [email protected] (C.W. Oosterlee).

Funding

✩ The research is financially supported by the Dutch Ministry of Economic Affairs under the Project BTS01044. E-mail addresses: [email protected] (Y.A. Erlangga), [email protected] (C. Vuik), [email protected] (C.W. Oosterlee).

Keywords

Helmholtz equation
ILU
Krylov subspace methods
Multigrid
Shifted-Laplace preconditioner

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10.1016/j.apnum.2005.04.039

Cite this

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title = "Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation",

abstract = "Within the framework of shifted-Laplace preconditioners [Y.A. Erlangga, C. Vuik, C.W. Oosterlee, On a class of preconditioners for the Helmholtz equation, Appl. Numer. Math. 50 (2004) 409-425] for the Helmholtz equation, different methods for the approximation of the inverse of a complex-valued Helmholtz operator are discussed. The performance of the preconditioner for Helmholtz problems at high wavenumbers in heterogeneous media is evaluated. Comparison with other preconditioners from the literature is also presented.",

keywords = "Helmholtz equation, ILU, Krylov subspace methods, Multigrid, Shifted-Laplace preconditioner",

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

note = "Funding Information: ✩ The research is financially supported by the Dutch Ministry of Economic Affairs under the Project BTS01044. E-mail addresses: [email protected] (Y.A. Erlangga), [email protected] (C. Vuik), [email protected] (C.W. Oosterlee).",

year = "2006",

month = may,

doi = "10.1016/j.apnum.2005.04.039",

language = "English",

volume = "56",

pages = "648--666",

journal = "Applied Numerical Mathematics",

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AU - Erlangga, Y. A.

AU - Vuik, C.

AU - Oosterlee, C. W.

N1 - Funding Information: ✩ The research is financially supported by the Dutch Ministry of Economic Affairs under the Project BTS01044. E-mail addresses: [email protected] (Y.A. Erlangga), [email protected] (C. Vuik), [email protected] (C.W. Oosterlee).

PY - 2006/5

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N2 - Within the framework of shifted-Laplace preconditioners [Y.A. Erlangga, C. Vuik, C.W. Oosterlee, On a class of preconditioners for the Helmholtz equation, Appl. Numer. Math. 50 (2004) 409-425] for the Helmholtz equation, different methods for the approximation of the inverse of a complex-valued Helmholtz operator are discussed. The performance of the preconditioner for Helmholtz problems at high wavenumbers in heterogeneous media is evaluated. Comparison with other preconditioners from the literature is also presented.

AB - Within the framework of shifted-Laplace preconditioners [Y.A. Erlangga, C. Vuik, C.W. Oosterlee, On a class of preconditioners for the Helmholtz equation, Appl. Numer. Math. 50 (2004) 409-425] for the Helmholtz equation, different methods for the approximation of the inverse of a complex-valued Helmholtz operator are discussed. The performance of the preconditioner for Helmholtz problems at high wavenumbers in heterogeneous media is evaluated. Comparison with other preconditioners from the literature is also presented.

KW - Helmholtz equation

KW - ILU

KW - Krylov subspace methods

KW - Multigrid

KW - Shifted-Laplace preconditioner

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DO - 10.1016/j.apnum.2005.04.039

M3 - Article

AN - SCOPUS:33644865436

SN - 0168-9274

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SP - 648

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 5

ER -

Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation

Abstract

Bibliographical note

Funding

Keywords

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