A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations

Handle URI:
http://hdl.handle.net/10754/597372
Title:
A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
Authors:
Poulson, Jack; Engquist, Björn; Li, Siwei; Ying, Lexing
Abstract:
A parallelization of a sweeping preconditioner for three-dimensional Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are shown to be O(γ2N4/3) and O(γN logN), where γ(ω) denotes the modestly frequency-dependent number of grid points per perfectly matched layer. Several computational and memory improvements are introduced relative to using black-box sparse-direct solvers for the auxiliary problems, and competitive runtimes and iteration counts are reported for high-frequency problems distributed over thousands of cores. Two open-source packages are released along with this paper: Parallel Sweeping Preconditioner (PSP) and the underlying distributed multifrontal solver, Clique. © 2013 Society for Industrial and Applied Mathematics.
Citation:
Poulson J, Engquist B, Li S, Ying L (2013) A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations. SIAM Journal on Scientific Computing 35: C194–C212. Available: http://dx.doi.org/10.1137/120871985.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
2-May-2013
DOI:
10.1137/120871985
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This work was partially supported by the sponsors of the Texas Consortium for Computational Seismology.The second author was supported by NSF grant DMS-1016577. The fourth author was supported by NSF CAREER grant DMS-0846501, NSF grant DMS-1016577, and funding from KAUST.This author was supported by a CAM fellowship.
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Full metadata record

DC FieldValue Language
dc.contributor.authorPoulson, Jacken
dc.contributor.authorEngquist, Björnen
dc.contributor.authorLi, Siweien
dc.contributor.authorYing, Lexingen
dc.date.accessioned2016-02-25T12:31:50Zen
dc.date.available2016-02-25T12:31:50Zen
dc.date.issued2013-05-02en
dc.identifier.citationPoulson J, Engquist B, Li S, Ying L (2013) A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations. SIAM Journal on Scientific Computing 35: C194–C212. Available: http://dx.doi.org/10.1137/120871985.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/120871985en
dc.identifier.urihttp://hdl.handle.net/10754/597372en
dc.description.abstractA parallelization of a sweeping preconditioner for three-dimensional Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are shown to be O(γ2N4/3) and O(γN logN), where γ(ω) denotes the modestly frequency-dependent number of grid points per perfectly matched layer. Several computational and memory improvements are introduced relative to using black-box sparse-direct solvers for the auxiliary problems, and competitive runtimes and iteration counts are reported for high-frequency problems distributed over thousands of cores. Two open-source packages are released along with this paper: Parallel Sweeping Preconditioner (PSP) and the underlying distributed multifrontal solver, Clique. © 2013 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis work was partially supported by the sponsors of the Texas Consortium for Computational Seismology.The second author was supported by NSF grant DMS-1016577. The fourth author was supported by NSF CAREER grant DMS-0846501, NSF grant DMS-1016577, and funding from KAUST.This author was supported by a CAM fellowship.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectHelmholtzen
dc.subjectParallelen
dc.subjectPreconditioneren
dc.subjectSweepingen
dc.subjectTime-harmonicen
dc.titleA Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equationsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
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