An optimized Schwarz waveform relaxation method for the unsteady convection diffusion equation in two dimensions

We are interested in solving time dependent problems using domain decomposition methods. In the classical approach, one discretizes first the time dimension and then one solves a sequence of steady problems by a domain decomposition method. In this paper, we treat directly the time dependent problem and we study a Schwarz waveform relaxation algorithm for the convection diffusion equation in two dimensions. We introduce the operators on the interfaces which minimize the convergence rate, resulting in an efficient method: numerical results illustrate the performances and show that the corresponding algorithms converge much faster than the classical one.