Space-time domain decomposition for parabolic problems
This paper concerns a space-time domain decomposition iteration for a model advection diffusion equation in one and two dimensions. The discretization of this iteration is the block red-black variant of the waveform relaxation method and some new convergence results for this scheme are obtained. The asymptotic convergence rate is superlinear and is governed by the diffusion of the error across the overlap between subdomains. It depends on the size of this overlap and the diffusion coefficient in the equation. The convergence rate for the heat equation in a large time window is initially linear and it deteriorates as the number of subdomains increases. The duration of the transient linear regime is propositional to the length of the time window. For advection dominated problems, the convergence rate is initially linear and it improves as the ratio of advection to diffusion increases. It is independent of the size of the time window and of the number of subdomains. Numerical examples are given.
scientific article; zbMATH DE number 1884035