Journal
NETWORKS AND HETEROGENEOUS MEDIA
Volume 5, Issue 3, Pages 487-505Publisher
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/nhm.2010.5.487
Keywords
Domain decomposition; Schwarz waveform relaxation; Semilinear reaction-diffusion equation; Nonlinear transmission conditions
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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
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