Schwarz Waveform Relaxation Methods for Systems of Semi-Linear Reaction-Diffusion Equations

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.
Document type :
Other publications
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00491292
Contributor : Victorita Dolean <>
Submitted on : Friday, June 11, 2010 - 9:28:34 AM
Last modification on : Thursday, May 3, 2018 - 1:32:55 PM
Long-term archiving on : Friday, September 17, 2010 - 1:48:07 PM

File

dolean_contrib.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00491292, version 1

Citation

Stephane Descombes, Victorita Dolean, Martin Gander. Schwarz Waveform Relaxation Methods for Systems of Semi-Linear Reaction-Diffusion Equations. 2010. ⟨hal-00491292⟩

Share

Metrics

Record views

414

Files downloads

182