A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations. 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(γ 2 N 4/3 ) and O(γNlogN), 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.
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References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
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- Zepeda-Núñez, Leonardo; Demanet, Laurent: The method of polarized traces for the 2D Helmholtz equation (2016)
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- Poulson, Jack; Engquist, Björn; Li, Siwei; Ying, Lexing: A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations (2013)