Space-Time Domain Decomposition Methods for Diffusion Problems in Mixed Formulations

This paper is concerned with global-in-time, nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem. Two approaches are considered: one uses the time-dependent Steklov–Poincaré operator and the other uses optimized Schwarz waveform relaxation (OSWR) based on Robin transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interfaces between subdomains is derived, and different time grids are employed to adapt to different time scales in the subdomains. Demonstrations of the wellposedness of the Robin subdomain problems involved in the OSWR method and a convergence proof of the OSWR algorithm are given for the mixed formulation. Numerical results for two-dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods.