Optimized Schwarz waveform relaxation and discontinuous Galerkin time stepping for heterogeneous problems

We design and analyze a Schwarz waveform relaxation algorithm for domain decomposition of advection-diffusion-reaction problems with strong heterogeneities. The interfaces are curved, and we use optimized Robin or Ventcell transmission conditions. We analyze the semi-discretization in time with Discontinuous Galerkin as well. We also show two-dimensional numerical results using generalized mortar finite elements in space.