New high-order, semi-implicit Hybridized Discontinuous Galerkin - Spectral Element Method (HDG-SEM) for simulation of complex wave propagation involving coupling between seismic, hydro-acoustic and infrasonic waves: numerical analysis and case studies.

Abstract:

New seismological monitoring networks combine broadband seismic receivers, hydrophones and micro-barometers antenna, providing complementary observation of source-radiated waves. Exploiting these observations requires accurate and multi-media – elastic, hydro-acoustic, infrasound - wave simulation methods, in order to improve our physical understanding of energy exchanges at material interfaces.

We present here a new development of a high-order Hybridized Discontinuous Galerkin (HDG) method, for the simulation of coupled seismic and acoustic wave propagation, within a unified framework ([1],[2]) allowing for continuous and discontinuous Spectral Element Methods (SEM) to be used in the same simulation, with conforming and non-conforming meshes. The HDG-SEM approximation leads to differential – algebraic equations, which can be solved implicitly using energy-preserving time-schemes.

The proposed HDG-SEM is computationally attractive, when compared with classical Discontinuous Galerkin methods, involving only the approximation of the single-valued traces of the velocity field along the element interfaces as globally coupled unknowns. The formulation is based on a variational approximation of the physical fluxes, which are shown to be the explicit solution of an exact Riemann problem at each element boundaries. This leads to a highly parallel and efficient unstructured and high-order accurate method, which can be space-and-time adaptive.

A numerical study of the accuracy and convergence of the HDG-SEM is performed through a number of case studies involving elastic-acoustic (infrasound) coupling with geometries of increasing complexity. Finally, the performance of the method is illustrated through realistic case studies involving ground wave propagation associated to topography effects.

In conclusion, we outline some on-going extensions of the method.

References:

[1] Cockburn, B., Gopalakrishnan, J., Lazarov, R., Unified hybridization of discontinuous Galerkin, mixed and continuous Galerkin methods for second order elliptic problems, SIAM J. Num. Anal., 47, 2, 1319-1365, 2009.

[2] Nguyen, N., Peraire, J., Cockburn, B., High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics, J. Comp. Physics, 230, 10, 3695-3718, 2011.