Two-level preconditioners for the Helmholtz equation

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

Research output: Chapter in Book/Report/Conference proceedingChapter

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

Publication series

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

Keywords

  • Helmholtz equation
  • two-level preconditioners

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  • Cite this

    Bonazzoli, M., Dolean, V., Graham, I. G., Spence, E. A., & Tournier, P-H. (Accepted/In press). Two-level preconditioners for the Helmholtz equation. In Lecture Notes in Computational Science and Engineering (Lecture Notes in Computational Science and Engineering). Springer.