Domain decomposition for wave propagation problems

The problem posed by domain decomposition methods is to find the correct modeling of physical phenomena across the interfaces separating the subdomains. The technique described here for wave propagation problems is based on physical grounds since it relies on the fact that the wave equation can be decomposed into incoming and outgoing wave modes at the boundaries of the subdomains. The inward propagating waves depend on the solution exterior to the subdomains and therefore are computed from the appropriate boundary conditions, while the behavior of the outward propagating waves is determined by the solution inside the subdomains. The technique is applied to the anisotropic-viscoelastic wave equation, which practically includes all the possible rheologies of one-phase media.