Optimal Schwarz waveform relaxation for fractional diffusion-wave equations

Abstract

We introduce domain decomposition methods of Schwarz waveform relaxation (WR) type for fractional diffusion-wave equations. We show that the Dirichlet transmission conditions among the subdomains lead to slow convergence. So, we construct optimal transmission conditions at the artificial interfaces and we prove that optimal Schwarz WR methods on N subdomains converge in N iterations both on infinite spatial domains and on finite spatial domains. We also propose optimal transmission conditions when the original problem is spatially discretized and we prove the same result found in the continuous case.