@inproceedings{98a56fd6a0b945a2adaadfcb56b020b5,
title = "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.",
keywords = "domain decomposition, domain decomposition method, nonlinear PDEs, linear convergence, convergence history",
author = "St{\'e}phane Descombes and Victorita Dolean and Gander, {Martin J.}",
year = "2010",
month = oct,
day = "29",
doi = "10.1007/978-3-642-11304-8_49",
language = "English",
isbn = "9783642113031",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
pages = "423--430",
editor = "Yunqing Huang and Ralf Kornhuber and Olof Widlund and Jinchao Xu",
booktitle = "Domain Decomposition Methods in Science and Engineering XIX",
note = "19th International Conference on Domain Decomposition, DD19 ; Conference date: 17-08-2009 Through 22-08-2009",
}