Space-time domain decomposition for mixed formulations of diffusion equations

International audienceThe far field simulation of underground nuclear waste disposal site requires a high computational cost due to the widely varying properties of different materials, the different length and time scales, and the high accuracy requirements. Nonoverlapping domain decomposition methods allow local adaptation in both space and time and result in parallel algorithms. We have extended the optimized Schwarz waveform relaxation (OSWR) method, successfully used for finite elements and finite volumes, to the case of mixed finite elements with their local mass-conservation property. Another choice is the substructuring method, which has been shown to be efficient for steady state problems with strong heterogeneities. We study a time-dependent Schur complement method, which is the algebraic counterpart of the discrete Steklov Poincaré operator, and introduce the Neumann preconditioner as well as weight matrices designed to make the convergence speed independent of the heterogeneities. Both methods enable the use of local time steps when the subdomains have highly different physical properties. Their performance is illustrated on test cases suggested by nuclear waste disposal problems