Multiphysics wave propagation with polytopal Discontinuous Galerkin methods

Michele Botti
MOX, Dipartimento di Matematica
Wednesday 9th November 2022
Aula Seminari III piano
In this seminar, we focus on the numerical analysis of a polygonal discontinuous Galerkin (PolyDG) scheme for the simulation of multiphysics wave propagation in heterogeneous media. We address wave phenomena in elastic, poroelastic, and acoustic materials coupled by means of physically consistent transmission conditions. The coupling terms also depend on the pores configuration at the interface between the subdomains. For all models configuration, we introduce the PolydG semi-discrete formulation, which is then coupled with implicit time marching schemes. The proposed PolyDG approximation offers a high-level of flexibility and precision thanks to its arbitrary-order accuracy and capability to support general meshes. We present a complete stability analysis and derive a-priori hp-error estimates. A wide set of verification tests and examples of physical interest are investigated in order to assess the performances of the method. This research work has been funded by the European Commission through the H2020-MSCA-IF-EF project PDGeoFF (Grant no. 896616) and by the Istituto Nazionale di Alta Matematica through the INdAM-GNCS project no. CUP-E55F22000270001. Contatto: