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 5 articles )
Showing results 1 to 5 of 5.
- Liu, Fei; Ying, Lexing: Recursive sweeping preconditioner for the three-dimensional Helmholtz equation (2016)
- Liu, Fei; Ying, Lexing: Additive sweeping preconditioner for the Helmholtz equation (2016)
- Vion, A.; Geuzaine, C.: Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem (2014)
- C.Stolk, Christiaan: A rapidly converging domain decomposition method for the Helmholtz equation (2013)
- Poulson, Jack; Engquist, Björn; Li, Siwei; Ying, Lexing: A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations (2013)