Global and Localized Parallel Preconditioning Techniques for Large Scale Solid Earth Simulations

Kai Wang, Sang-Bae Kim, Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Kengo Nakajima
Research Organization for Information Science and Technology (RIST)
2-2-54 Naka-Meguro, Meguro-ku
Tokyo 153--0061, Japan

Hiroshi Okuda
Department of Quantum Engineering and Systems Science
The University of Tokyo
7-3-1 Hongo Bunkyo-ku
Tokyo 113--8656, Japan

Abstract

We investigate and compare a few parallel preconditioning techniques in the iterative solution of large sparse linear systems arising from solid Earth simulation with and without using contact information in the domain partitioning process. Previous studies are focused on using static or matrix pattern based incomplete LU (ILU) preconditioners in a localized preconditioner implementation. Our current studies are concerned about preconditioner performance for solving two different problem configurations with and without known contact information. For the cases with contact information, we use localized threshold value based incomplete LU (ILUT) preconditioner to improve efficiency. For the cases without contact information, we use a global sparse approximate inverse preconditioner with a static sparsity pattern to achieve robustness. Numerical results from simulating ground motion on a parallel supercomputer are given to compare the effectiveness of these parallel preconditioning techniques.


Key words: Solid Earth simulation, fault contact problem, sparse matrices, preconditioning techniques.

Mathematics Subject Classification: ***


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This paper has been published in Future Generation Computer Systems, Vol. 19, No. 4, pp/ 443 - 456 (2003).

Technical Report 345-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.

This research work was supported in part by the Japan Research Organization for Information Science & Technology (RIST), in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, in part by the U.S. Department of Energy under grant DE-FG02-02ER45961, and in part by the University of Kentucky Research Committee.