Hybridizable discontinuous Galerkin method for the two-dimensional frequency-domain elastic wave equations

Discontinuous Galerkin (DG) methods are nowadays actively studied and increasingly exploited for the simulation of large-scale time-domain (i.e. unsteady) seismic wave propagation problems. Although theoretically applicable to frequency-domain problems as well, their use in this context has been hampered by the potentially large number of coupled unknowns they incur, especially in the three-dimensional case, as compared to classical continuous finite element methods. In this paper, we address this issue in the framework of so-called hybridizable discontinuous Galerkin (HDG) formulations. As a first step, we study a HDG method for the resolution of the frequency-domain elastic wave equations in the two-dimensional case. We describe the weak formulation of the method and provide some implementation details. The proposed HDG method is assessed numerically including a comparison with a classical upwind flux-based DG method, showing better overall computational efficiency as a result of the drastic reduction of the number of globally coupled unknowns in the resulting discrete HDG system.