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

4 Citations (Scopus)

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 publicationDomain Decomposition Methods in Science and Engineering XXIV. DD 2017
EditorsP. Bjorstad
Place of PublicationCham, Switzerland
PublisherSpringer Verlag
Pages139-147
Number of pages9
ISBN (Electronic)9783319938738
ISBN (Print)9783319938721
DOIs
Publication statusPublished - 1 Jan 2018

Publication series

NameLecture Notes in Computational Science and Engineering
Volume125
ISSN (Print)1439-7358

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

Cite this

Bonazzoli, M., Dolean, V., Graham, I. G., Spence, E. A., & Tournier, P. H. (2018). Two-level preconditioners for the helmholtz equation. In P. Bjorstad (Ed.), Domain Decomposition Methods in Science and Engineering XXIV. DD 2017 (pp. 139-147). (Lecture Notes in Computational Science and Engineering; Vol. 125). Cham, Switzerland: Springer Verlag. https://doi.org/10.1007/978-3-319-93873-8_11