Trefftz-Discontinuous Galerkin Approach for Solving Elastodynamic Problem
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.
This work is supported by the Inria—Total S.A. strategic action “Depth Imaging Partnership” (http://dip.inria.fr).
- 1.E. Trefftz, Ein Gegenstuck zum Ritzschen Verfahren, in Proceedings of the 2nd International Congress of Applied Mechanics, Zurich (1926), pp. 131–137Google Scholar
- 3.O.C. Zienkiewic, Trefftz type approximation and the generalized finite element method - history and development. Comput. Assist. Mech. Eng. Sci. 4, 305–316 (1997)Google Scholar
- 18.P. Le Tallec, Modélisation et calcul des milieux continus (Editions Ecole Polytechnique, Palaiseau, 2009)Google Scholar
- 20.H. Barucq, H. Calandra, J. Diaz, E. Shishenina, Space-time Trefftz - discontinuous Galerkin approximation for elasto-acoustics. Inria Bordeaux Sud-Ouest, LMAP CNRS, Total EP, RR-9104 (2017)Google Scholar