Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | C194-C212 |
| Number of pages | 1 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 35 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 2 2013 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: This 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.