Block filtering decomposition

SUMMARYThis 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...

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Bibliographic Details
Published in:Numerical linear algebra with applications Vol. 21; no. 6; pp. 703 - 721
Main Authors: Fezzani, Riadh, Grigori, Laura, Nataf, Frédéric, Wang, Ke
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.12.2014
Wiley Subscription Services, Inc
Wiley
Subjects:
block incomplete decomposition
Computer Science
Convergence
Decomposition
Discretization
Distributed, Parallel, and Cluster Computing
Filtering
filtering property
Filtration
Iterative methods
Krylov subspace methods
linear solvers
Mathematical analysis
Mathematics
Numerical Analysis
preconditioning
Vectors (mathematics)
ISSN:1070-5325, 1099-1506
Online Access:Get full text
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Summary:SUMMARYThis 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 that 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. We show the efficiency of our preconditioner through a set of numerical experiments on symmetric and nonsymmetric matrices. Copyright © 2014 John Wiley & Sons, Ltd.
Bibliography:ark:/67375/WNG-68T4TMQN-4
istex:4A38B4F3533385017F673FF13F116CE82A9E4DEB
ArticleID:NLA1921
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
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ISSN:1070-5325
1099-1506
DOI:10.1002/nla.1921