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

Abstract

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 well-posedness 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.