Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations

Victorita Dolean, Martin J. Gander, Erwin Veneros, Hui Zhang

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

1 Citation (Scopus)

Abstract

Both the Helmholtz equation and the time-harmonic Maxwell’s equations are difficult to solve by iterative methods in the intermediate to high frequency regime, and domain decomposition methods are among the most promising techniques for this task. We focus here on the case of dissipative and conductive media with strongly heterogeneous coefficients, and develop optimized transmission conditions for this case. We establish a link for the use of such conditions between the case of Helmholtz and Maxwell’s equations, and show that in both cases jumps aligned with the interfaces of the subdomains can improve the convergence of the subdomain iteration.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXIII
Place of PublicationBerlin
PublisherSpringer-Verlag
Pages145-152
Number of pages8
ISBN (Print)9783319523880, 9783319523897
DOIs
Publication statusPublished - 18 Mar 2017
Event23rd International Conference on Domain Decomposition Methods, DD23 - Jeju Island, Korea, Republic of
Duration: 6 Jul 201510 Jul 2015

Publication series

NameLecture Notes in Computational Science and Engineering
Volume116
ISSN (Print)1439-7358

Conference

Conference23rd International Conference on Domain Decomposition Methods, DD23
CountryKorea, Republic of
City Jeju Island
Period6/07/1510/07/15

Keywords

  • discontinuous coefficients
  • Helmholtz equation
  • Maxwell’s equations
  • optimized Schwarz methods

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  • Cite this

    Dolean, V., Gander, M. J., Veneros, E., & Zhang, H. (2017). Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations. In Domain Decomposition Methods in Science and Engineering XXIII (pp. 145-152). (Lecture Notes in Computational Science and Engineering; Vol. 116). Springer-Verlag. https://doi.org/10.1007/978-3-319-52389-7_13