Abstract
We present a parallel implementation of Engquist and Ying's sweeping preconditioner, which exploits radiation boundary conditions in order to form an approximate block LDLT factorization of the Helmholtz operator with only O(N4/3) work and an application (and memory) cost of only O(N logN). The approximate factorization is then used as a preconditioner for GMRES, and we show that essentially O(1) iterations are required for convergence, even for the full SEG/EAGE over-thrust model at 30 Hz. In particular, we demonstrate the solution of said problem in a mere 15 minutes on 8192 cores of TACC's Lonestar, which may be the largest-scale 3D heterogeneous Helmholtz calculation to date. Generalizations of our parallel strategy are also briefly discussed for time-harmonic linear elasticity and Maxwell's equations.
| Original language | English (US) |
|---|---|
| Title of host publication | SEG Technical Program Expanded Abstracts 2012 |
| Publisher | Society of Exploration Geophysicists |
| Pages | 3200-3205 |
| Number of pages | 6 |
| ISBN (Print) | 9781622769452 |
| DOIs | |
| State | Published - Oct 25 2012 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: The authors thank TACC for access to Lonestar, and particularly Bill Barth for suggesting that we enforce local memory allocations and Tommy Minyard for organizing the large runs. We also thank Sergey Fomel, Anshul Gupta, Edgar Solomonik, and Laura Grigori for helpful discussions. The work is financially supported by KAUST and the TCCS sponsors.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.