25th Annual GAMM-Seminar Leipzig on

FEM and BEM for time-dependent wave problems

Coupling Discontinuous Galerkin Methods and Retarded Potentials for Time Dependent Wave Propagation Problems

Patrick Joly (INRIA Paris - Rocquencourt)

This work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities. To do so, we propose to combine a discretization based on a discontinuous Galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain. The coupling formula enforces a discrete energy identity ensuring the stability under the usual CFL condition on the interior. Moreover, the scheme allows to use a smaller time step in the interior domain yielding to quasi-optimal discretization parameters for both methods. The aliasing phenomena introduced by the local time stepping is reduced by a post-processing by averaging in time obtaining a stable and second order consistent coupling algorithm. The construction and the main theoretical properties of the method will be presented during the conference. I will also show some numerical experiments on academic problems that show the feasibility of the whole discretization procedure.

Impressum Valid HTML 4.0 Transitional