On Mathematical and Numerical Modelling of Multiphysics Wave Propagation with Polytopal Discontinuous Galerkin Methods: a Review

Abstract In this work we review discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. particular, address elastic, poro-elastic, and poro-elasto-acoustic materials. Wave is modeled by using either elastodynamics equation elastic domain, acoustics equations acoustic domain low-frequency Biot’s poro-elastic one. The coupling between different models realized means (physically consistent) transmission conditions, weakly imposed at interface subdomains. For all configuration, introduce analyse PolydG semi-discrete formulation, which then coupled with suitable time marching schemes. problem, present stability analysis derive a-priori error estimates a energy norm. A wide set two-dimensional verification tests manufactured solutions are presented order to validate analysis. Examples physical interest also shown demonstrate capability proposed methods.