A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations
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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.
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.
SponsorsThis 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.