A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations

A parallelization of a sweeping preconditioner for 3D 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({\gamma}^2 N^{4/3}) and O({\gamma} N log N), wher...

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Bibliographic Details
Published in:arXiv.org 2013-02
Main Authors: Poulson, Jack, Engquist, Björn, Li, Siwei, Lexing Ying
Format: Article
Language:English
Subjects:
Computer memory
Helmholtz equations
Iterative methods
Parallel processing
Perfectly matched layers
Solvers
Sweeping
Online Access:Get full text
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Summary:A parallelization of a sweeping preconditioner for 3D 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({\gamma}^2 N^{4/3}) and O({\gamma} N log N), where {\gamma}({\omega}) 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".
ISSN:2331-8422
DOI:10.48550/arxiv.1204.0111