Two-level preconditioners for the Helmholtz equation - Archive ouverte HAL
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Chapitre D'ouvrage Année : 2018
Two-level preconditioners for the Helmholtz equation
Marcella Bonazzoli (1) , Victorita Dolean (2, 1) , Ivan G. Graham (3) , Euan A. Spence (3) , Pierre-Henri Tournier (4, 5)
1 LJAD - Laboratoire Jean Alexandre Dieudonné (Université Côte d'Azur U.M.R. no 7351 du C.N.R.S. Parc Valrose 06108 Nice Cedex 02 France - France)
"> LJAD - Laboratoire Jean Alexandre Dieudonné
2 Department of Mathematics and Statistics [Univ Strathclyde] (Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH - Royaume-Uni)
"> Department of Mathematics and Statistics [Univ Strathclyde]
3 Department of Mathematical Sciences [Bath] (Claverton Down Bath BA2 7AY - Royaume-Uni)
"> Department of Mathematical Sciences [Bath]
4 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Université, Boîte courrier 187 - 75252 Paris Cedex 05 - France)
"> LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
5 ALPINES - Algorithms and parallel tools for integrated numerical simulations (France) "> ALPINES - Algorithms and parallel tools for integrated numerical simulations

Résumé

In this paper we compare numerically two different coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation, both in two and three dimensions. While we solve the pure Helmholtz problem without absorption, the preconditioners are built from problems with absorption. In the first method, the coarse space is based on the discretization of the problem with absorption on a coarse mesh, with diameter constrained by the wavenumber. In the second method, the coarse space is built by solving local eigenproblems involving the Dirichlet-to-Neumann (DtN) operator.

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Analyse numérique [math.NA]
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https://hal.science/hal-01525424

Soumis le : mercredi 21 février 2018-16:26:05

Dernière modification le : jeudi 12 décembre 2024-03:43:22

Archivage à long terme le : mardi 22 mai 2018-14:37:40

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Dates et versions

hal-01525424 , version 1 (20-05-2017)
hal-01525424 , version 2 (08-11-2017)
hal-01525424 , version 3 (21-02-2018)
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Marcella Bonazzoli, Victorita Dolean, Ivan G. Graham, Euan A. Spence, Pierre-Henri Tournier. Two-level preconditioners for the Helmholtz equation. Domain Decomposition Methods in Science and Engineering XXIV, 125, pp.139-147, 2018, Lecture Notes in Computational Science and Engineering, ⟨10.1007/978-3-319-93873-8_11⟩. ⟨hal-01525424v3⟩

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