Two-level preconditioners for the Helmholtz equation

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Bonazzoli, Marcella and Dolean, Victorita and Graham, Ivan G. and Spence, Euan A. and Tournier, Pierre-Henri; Bjørstad, P. E., ed. (2019) Two-level preconditioners for the Helmholtz equation. In: Domain Decomposition Methods in Science and Engineering XXIV (DD 2017). Lecture Notes in Computational Science and Engineering, 125 . Springer, NOR, pp. 139-147. ISBN 9783319938738 (https://doi.org/10.1007/978-3-319-93873-8_11)

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Abstract

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.

ORCID iDs

Bonazzoli, Marcella, Dolean, Victorita ORCID logoORCID: https://orcid.org/0000-0002-5885-1903, Graham, Ivan G., Spence, Euan A. and Tournier, Pierre-Henri; Bjørstad, P. E.
  • Item type:Book Section
    ID code:64650
    Dates:
    Date
    Event
    5 January 2019
    Published
    21 February 2018
    Accepted
    23 May 2017
    Submitted
    Notes:© 2018 Springer International Publishing AG, part of Springer Nature Bonazzoli, M., Dolean, V., Graham, I.G., Spence, E.A., Tournier, PH. (2018). Two-Level Preconditioners for the Helmholtz Equation. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_11
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:02 Jul 2018 10:25
    Last modified:11 Nov 2024 15:14
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/64650
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