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Generalized Filtering Decomposition

Laura Grigori 1 Frédéric Nataf 2
1 GRAND-LARGE - Global parallel and distributed computing
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LIFL - Laboratoire d'Informatique Fondamentale de Lille, LRI - Laboratoire de Recherche en Informatique
Abstract : This paper introduces a new preconditioning technique that is suitable for matrices arising from the discretization of a system of PDEs on unstructured grids. The preconditioner satisfies a so-called filtering property, which ensures that the input matrix is identical with the preconditioner on a given filtering vector. This vector is chosen to alleviate the effect of low frequency modes on convergence and so decrease or eliminate the plateau which is often observed in the convergence of iterative methods. In particular, the paper presents a general approach that allows to ensure that the filtering condition is satisfied in a matrix decomposition. The input matrix can have an arbitrary sparse structure. Hence, it can be reordered using nested dissection, to allow a parallel computation of the preconditioner and of the iterative process.
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Submitted on : Tuesday, March 15, 2011 - 3:45:50 PM
Last modification on : Thursday, July 8, 2021 - 3:51:01 AM
Long-term archiving on: : Thursday, June 16, 2011 - 3:03:21 AM

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  • HAL Id : inria-00576894, version 1
  • ARXIV : 1103.3026

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Laura Grigori, Frédéric Nataf. Generalized Filtering Decomposition. [Research Report] RR-7569, INRIA. 2011, pp.8. ⟨inria-00576894⟩

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