Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains

Authors:
Toufic Abboud;Patrick Joly;Jerónimo Rodrıguez;Isabelle Terrasse
Affiliations:
CMAP Ecole Polytechnique, 91128 Palaiseau, France;POEMS, UMR 7231, CNRS-INRIA-ENSTA, INRIA Rocquencourt, Domaine de Voluceau, BP105, Le Chesnay, France;POEMS, UMR 7231, CNRS-INRIA-ENSTA, INRIA Rocquencourt, Domaine de Voluceau, BP105, Le Chesnay, France and Departamento de Matemática Aplicada, Facultad de Matemáticas, USC, 15782 Santiag ...;EADS-CCR, BP 76, 92152 Suresnes, France
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

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 in 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 are reduced by a post-processing by averaging in time obtaining a stable and second order consistent (in time) coupling algorithm. We compute the numerical rate of convergence of the method for an academic problem. The numerical results show the feasibility of the whole discretization procedure.