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Block filtering decomposition

Riadh Fezzani 1 Laura Grigori 2, 3 Frédéric Nataf 2, 3 Ke Wang 4 
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
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 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.
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Submitted on : Friday, December 5, 2014 - 4:18:21 AM
Last modification on : Friday, January 21, 2022 - 3:21:49 AM

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Riadh Fezzani, Laura Grigori, Frédéric Nataf, Ke Wang. Block filtering decomposition. Numerical Linear Algebra with Applications, 2014, 21 (6), pp.18. ⟨10.1002/nla.1921⟩. ⟨hal-01091252⟩



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