Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations

Filipa Caetano; Martin J. Gander; Laurence Halpern; Jérémie Szeftel; Filipa Caetano; Martin J. Gander; Laurence Halpern; Jérémie Szeftel

doi:10.3934/nhm.2010.5.487

Networks and Heterogeneous Media

2010, Volume 5, Issue 3: 487-505. doi: 10.3934/nhm.2010.5.487

Previous Article Next Article

Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations

1.
Univ. Paris-Sud, Département de Mathématiques, CNRS, F-91405 Orsay
2.
Section de Mathématiques, Université de Genève, CP 64, 1211 Genève
3.
Université Paris 13, CNRS, UMR 7539 LAGA, 99 av. Jean-Baptiste Clément, F-93430 Villetaneuse
4.
DMA, Ecole Normale Supérieure, 45 rue d’Ulm, Paris

Received: 01 January 2010 Revised: 01 May 2010
35K55, 65M12, 65M55.

We introduce nonoverlapping domain decomposition algorithms of Schwarz waveform relaxation type for the semilinear reaction-diffusion equation. We define linear Robin and second order (or Ventcell) transmission conditions between the subdomains, which we prove to lead to a well defined and converging algorithm. We also propose nonlinear transmission conditions. Both types are based on best approximation problems for the linear equation and provide efficient algorithms, as the numerical results that we present here show.
- Domain decomposition,
- Schwarz waveform relaxation,
- Semilinear reaction-diffusion equation,
- Nonlinear transmission conditions
Citation: Filipa Caetano, Martin J. Gander, Laurence Halpern, Jérémie Szeftel. Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations[J]. Networks and Heterogeneous Media, 2010, 5(3): 487-505. doi: 10.3934/nhm.2010.5.487

Related Papers:
Abstract

We introduce nonoverlapping domain decomposition algorithms of Schwarz waveform relaxation type for the semilinear reaction-diffusion equation. We define linear Robin and second order (or Ventcell) transmission conditions between the subdomains, which we prove to lead to a well defined and converging algorithm. We also propose nonlinear transmission conditions. Both types are based on best approximation problems for the linear equation and provide efficient algorithms, as the numerical results that we present here show.
Reader Comments

Your name:*

Email:*
© 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)