Two-level preconditioners for the Helmholtz equation

Marcella Bonazzoli, Victorita Dolean, Ivan G. Graham, Euan A. Spence, Pierre-Henri Tournier

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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.
Original languageEnglish
Title of host publicationLecture Notes in Computational Science and Engineering
Place of PublicationCham, Switzerland
Publication statusAccepted/In press - 21 Feb 2018

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358


  • Helmholtz equation
  • two-level preconditioners

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