A Parallel Sweeping Preconditioner for Heterogeneous 3D Helmholtz Equations

Jack Poulson, Björn Engquist, Siwei Li, Lexing Ying

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)C194-C212
Number of pages1
JournalSIAM Journal on Scientific Computing
Issue number3
StatePublished - May 2 2013
Externally publishedYes


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