Trefftz -Discontinuous Galerkin Approach for Solving Elastodynamic Problem

Hélène Barucq 1 Henri Calandra 2 Julien Diaz 1 Elvira Shishenina 1, 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : Methods based on Discontinuous Finite Element approximation (DG FEM) are basically well-adapted to specifics of wave propagation problems in complex media, due to their numerical accuracy and flexibility. However, they still lack of computational efficiency, by reason of the high number of degrees of freedom required for simulations. The Trefftz-DG solution methodology investigated in this work is based on a formulation which is set only at the boundaries of the mesh. It is a consequence of the choice of test functions that are local solutions of the problem. It owns the important feature of involving a space-time approximation which requires using elements defined in the space-time domain. Herein, we address the Trefftz-DG solution of the Elastodynamic System. We establish its well-posedness which is based on mesh-dependent norms. It is worth noting that we employ basis functions which are space-time polynomial. Some numerical experiments illustrate the proper functioning of the method.
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Hélène Barucq, Henri Calandra, Julien Diaz, Elvira Shishenina. Trefftz -Discontinuous Galerkin Approach for Solving Elastodynamic Problem. ENUMATH 2017 - European Conference on Numerical Mathematics and Advanced Applications, Sep 2017, Voss, Norway. ⟨hal-01691617v2⟩

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