On the Dirichlet-to-Neumann coarse space for solving the Helmholtz problem using domain decomposition

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Abstract

We examine the use of the Dirichlet-to-Neumann coarse space within an additive Schwarz method to solve the Helmholtz equation in 2D. In particular, we focus on the selection of how many eigenfunctions should go into the coarse space. We find that wave number independent convergence of a preconditioned iterative method can be achieved in certain special cases with an appropriate and novel choice of threshold in the selection criteria. However, this property is lost in a more general setting, including the heterogeneous problem. Nonetheless, the approach converges in a small number of iterations for the homogeneous problem even for relatively large wave numbers and is robust to the number of subdomains used.
Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2019
Subtitle of host publicationEuropean Conference, Egmond aan Zee, The Netherlands, September 30 - October 4
Place of PublicationCham, Switzerland
PublisherSpringer
ISBN (Print)978-3-030-55873-4
Publication statusAccepted/In press - 1 Mar 2020
EventEuropean Numerical Mathematics and Advanced Applications Conference 2019 - Egmond aan Zee, Netherlands
Duration: 30 Sep 20194 Oct 2019
https://www.enumath2019.eu/

Conference

ConferenceEuropean Numerical Mathematics and Advanced Applications Conference 2019
Abbreviated titleENUMATH 2019
CountryNetherlands
CityEgmond aan Zee
Period30/09/194/10/19
Internet address

Keywords

  • Dirichlet-to-Neumann mapping
  • domain decomposition
  • Helmholt problem

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