Schwarz waveform relaxation methods for systems of semi-linear reaction-diffusion equations

Stéphane Descombes, Victorita Dolean, Martin J. Gander

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

2 Citations (Scopus)

Abstract

Schwarz waveform relaxation methods have been studied for a wide range of scalar linear partial differential equations (PDEs) of parabolic and hyperbolic type. They are based on a space-time decomposition of the computational domain and the subdomain iteration uses an overlapping decomposition in space. There are only few convergence studies for non-linear PDEs. We analyze in this paper the convergence of Schwarz waveform relaxation applied to systems of semi-linear reaction-diffusion equations. We show that the algorithm converges linearly under certain conditions over long time intervals. We illustrate our results, and further possible convergence behavior, with numerical experiments.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XIX
EditorsYunqing Huang, Ralf Kornhuber, Olof Widlund, Jinchao Xu
Place of PublicationLondon
PublisherSpringer
Pages423-430
Number of pages8
ISBN (Print)9783642113031
DOIs
Publication statusPublished - 29 Oct 2010
Event19th International Conference on Domain Decomposition, DD19 - Zhanjiajie, China
Duration: 17 Aug 200922 Aug 2009

Publication series

NameLecture Notes in Computational Science and Engineering
Volume78
ISSN (Print)1439-7358

Conference

Conference19th International Conference on Domain Decomposition, DD19
CountryChina
CityZhanjiajie
Period17/08/0922/08/09

Keywords

  • domain decomposition
  • domain decomposition method
  • nonlinear PDEs
  • linear convergence
  • convergence history

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  • Cite this

    Descombes, S., Dolean, V., & Gander, M. J. (2010). Schwarz waveform relaxation methods for systems of semi-linear reaction-diffusion equations. In Y. Huang, R. Kornhuber, O. Widlund, & J. Xu (Eds.), Domain Decomposition Methods in Science and Engineering XIX (pp. 423-430). (Lecture Notes in Computational Science and Engineering; Vol. 78). Springer. https://doi.org/10.1007/978-3-642-11304-8_49