Why classical schwarz methods applied to certain hyperbolic systems converge even without overlap

Victorita Dolean, Martin J. Gander

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

5 Citations (Scopus)
2 Downloads (Pure)

Abstract

Overlap is essential for the classical Schwarz method to be convergent when solving elliptic problems. Over the last decade, it was however observed that when solving systems of hyperbolic partial differential equations, the classical Schwarz method can be convergent even without overlap. We show that the classical Schwarz method without overlap applied to the Cauchy-Riemann equations which represent the discretization in time of such a system, is equivalent to an optimized Schwarz method for a related elliptic problem, and thus must be convergent, since optimized Schwarz methods are well known to be convergent without overlap.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XVII
PublisherSpringer
Pages467-475
Number of pages9
Volume60
ISBN (Print)9783540751984
DOIs
Publication statusPublished - 1 Dec 2008
Event17th International Conference on Domain Decomposition Methods - St. Wolfgang /Strobl, Austria
Duration: 3 Jul 20067 Jul 2006

Publication series

NameLecture Notes in Computational Science and Engineering
Volume60
ISSN (Print)1439-7358

Conference

Conference17th International Conference on Domain Decomposition Methods
CountryAustria
CitySt. Wolfgang /Strobl
Period3/07/067/07/06

Keywords

  • domain decomposition methods
  • partial differential equations
  • Cauchy-Riemann equations
  • discretization
  • elliptic problems
  • hyperbolic partial differential equation
  • hyperbolic system
  • Schwarz method

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  • Cite this

    Dolean, V., & Gander, M. J. (2008). Why classical schwarz methods applied to certain hyperbolic systems converge even without overlap. In Domain Decomposition Methods in Science and Engineering XVII (Vol. 60, pp. 467-475). (Lecture Notes in Computational Science and Engineering; Vol. 60). Springer. https://doi.org/10.1007/978-3-540-75199-1_59