# Sparse approximations of the Schur complement for parallel algebraic hybrid linear solvers in 3D

* Auteur correspondant
1 HiePACS - High-End Parallel Algorithms for Challenging Numerical Simulations
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest
Abstract : In this report we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems. In earlier works, the local Schur complements were computed exactly using a sparse direct solver. The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems. In this work we investigate the use of sparse approximation of the dense local Schur complements. These approximations are computed using a partial incomplete $LU$ factorization. Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems; preliminary experiments on linear systems arising from structural mechanics are also reported.
Type de document :
Rapport
[Research Report] RR-7237, INRIA. 2010, pp.18
Domaine :
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Littérature citée [15 références]

https://hal.inria.fr/inria-00466828
Contributeur : Luc Giraud <>
Soumis le : mardi 6 avril 2010 - 15:48:11
Dernière modification le : jeudi 11 janvier 2018 - 06:22:35
Document(s) archivé(s) le : mardi 14 septembre 2010 - 17:37:33

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RR-7237.pdf
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• HAL Id : inria-00466828, version 1

### Citation

Luc Giraud, Azzam Haidar, Yousef Saad. Sparse approximations of the Schur complement for parallel algebraic hybrid linear solvers in 3D. [Research Report] RR-7237, INRIA. 2010, pp.18. 〈inria-00466828〉

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