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Memory Optimization to Build a Schur Complement in an Hybrid Solver

Astrid Casadei 1, 2 Pierre Ramet 1, 2 
2 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : Solving linear system $Ax=b$ in parallel where $A$ is a large sparse matrix is a very recurrent problem in numerical simulations. One of the state-of-the-art most promising algorithm is the hybrid method based on domain decomposition and Schur complement. In this method, a direct solver is used as a subroutine on each subdomain matrix. This approach is subject to serious memory overhead. In this paper, we investigate new techniques to reduce memory consumption during the build of the Schur complement by a direct solver. Our method allows memory peak reduction from 10% to 30% on each processus for typical test cases.
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Submitted on : Thursday, May 24, 2012 - 4:24:33 PM
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Astrid Casadei, Pierre Ramet. Memory Optimization to Build a Schur Complement in an Hybrid Solver. [Research Report] RR-7971, INRIA. 2012, pp.11. ⟨hal-00700053v2⟩

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