A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation

C. D. Riyanti; A. Kononov; Y. A. Erlangga; C. Vuik; C. W. Oosterlee; R. E. Plessix; W. A. Mulder

doi:10.1016/j.jcp.2007.03.033

A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation

C. D. Riyanti^*, A. Kononov, Y. A. Erlangga, C. Vuik, C. W. Oosterlee, R. E. Plessix, W. A. Mulder

^*Corresponding author for this work

Sub Condensed Matter and Interfaces

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

Abstract

We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined with the Bi-CGSTAB iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator. A 3D multigrid method with 2D semi-coarsening is employed. We show numerical results for large problems arising in geophysical applications.

Original language	English
Pages (from-to)	431-448
Number of pages	18
Journal	Journal of Computational Physics
Volume	224
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2007.03.033
Publication status	Published - 20 May 2007

Keywords

Helmholtz equation
Krylov subspace method
Multigrid method
Preconditioner

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10.1016/j.jcp.2007.03.033

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@article{8ffac8e7ed054d689e56e64f7ae8c046,

title = "A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation",

abstract = "We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined with the Bi-CGSTAB iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator. A 3D multigrid method with 2D semi-coarsening is employed. We show numerical results for large problems arising in geophysical applications.",

keywords = "Helmholtz equation, Krylov subspace method, Multigrid method, Preconditioner",

author = "Riyanti, {C. D.} and A. Kononov and Erlangga, {Y. A.} and C. Vuik and Oosterlee, {C. W.} and Plessix, {R. E.} and Mulder, {W. A.}",

note = "Funding Information: This work is part of a joint Project between Philips and Shell on “Rigorous modeling of 3D wave propagation in inhomogeneous media for geophysical and optical problems”. This Project was financially supported by the Dutch Ministry of Economic Affairs under Project number BTS01044. We thank SARA Computing and Networking Services ( www.sara.nl ) in Amsterdam, the Netherlands for giving permission to implement and execute our parallel code using the SGI Altix 3700 Aster and SGI Origin 3800 Teras systems. ",

year = "2007",

month = may,

day = "20",

doi = "10.1016/j.jcp.2007.03.033",

language = "English",

volume = "224",

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journal = "Journal of Computational Physics",

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T1 - A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation

AU - Riyanti, C. D.

AU - Kononov, A.

AU - Erlangga, Y. A.

AU - Vuik, C.

AU - Oosterlee, C. W.

AU - Plessix, R. E.

AU - Mulder, W. A.

N1 - Funding Information: This work is part of a joint Project between Philips and Shell on “Rigorous modeling of 3D wave propagation in inhomogeneous media for geophysical and optical problems”. This Project was financially supported by the Dutch Ministry of Economic Affairs under Project number BTS01044. We thank SARA Computing and Networking Services ( www.sara.nl ) in Amsterdam, the Netherlands for giving permission to implement and execute our parallel code using the SGI Altix 3700 Aster and SGI Origin 3800 Teras systems.

PY - 2007/5/20

Y1 - 2007/5/20

N2 - We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined with the Bi-CGSTAB iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator. A 3D multigrid method with 2D semi-coarsening is employed. We show numerical results for large problems arising in geophysical applications.

AB - We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined with the Bi-CGSTAB iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator. A 3D multigrid method with 2D semi-coarsening is employed. We show numerical results for large problems arising in geophysical applications.

KW - Helmholtz equation

KW - Krylov subspace method

KW - Multigrid method

KW - Preconditioner

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M3 - Article

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SN - 0021-9991

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SP - 431

EP - 448

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation

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Keywords

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