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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 95
PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING
Edited by:
Paper 37

Parallel Preconditioners for Saddle-Point Problems

M. Ferronato, C. Janna and G. Gambolati

DMMMSA, University of Padova, Italy

Full Bibliographic Reference for this paper
M. Ferronato, C. Janna, G. Gambolati, "Parallel Preconditioners for Saddle-Point Problems", in , (Editors), "Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 37, 2011. doi:10.4203/ccp.95.37
Keywords: iterative methods, parallel preconditioning, saddle-point problems.

Summary

A desirable choice for approximating the (1,1) block and the Schur complement relies on "naturally" parallel strategies, such as the factorized sparse approximate inverse (FSAI) [4], which however may prove generally much less effective than incomplete factorizations for several problems. A recent development in the field of parallel preconditioners for symmetric positive definite problems is the block FSAI incomplete Cholesky (BFSAI-IC) algorithm [5]. BFSAI-IC is a hybrid preconditioner coupling a novel approximate inverse based on the FSAI concept with a block diagonal incomplete factorization, proving generally superior to more traditional parallel preconditioners for any number of computing cores. The present work describes a novel parallel implementation of the inexact constraint preconditioner (ParICP) making use of BFSAI-IC as preconditioning kernel. The performance of ParICP with the symmetric quasi-minimal residual (SQMR) solver is experimented with in large size saddle-point problems arising from the finite element integration of the coupled consolidation equations. The results show that ParICP is a very efficient implementation of constraint preconditioning for high performance computing. In ill-conditioned saddle-point problems, ParICP appears to be a very promising and robust tool to obtain accurate solutions within a reasonable time.

References
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L. Bergamaschi, M. Ferronato, G. Gambolati, "Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations", Computer Methods in Applied Mechanics and Engineering, 196, 2647-2656, 2007. doi:10.1016/j.cma.2007.01.013
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C. Janna, M. Ferronato, G. Gambolati, "A block FSAI-ILU parallel preconditioner for symmetric positive definite linear systems", SIAM Journal on Scientific Computing, 32, 2468-2484, 2010. doi:10.1137/090779760

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