Hybridizable discontinuous Galerkin method for the 2-D frequency-domain elastic wave equations. Issue 1 (13th December 2017)

• Record Type: Journal Article
• Authors: Bonnasse-Gahot, Marie; Calandra, Henri; Diaz, Julien; Lanteri, Stéphane
• Is Part Of: Geophysical journal international. Volume 213:Issue 1(2018:Apr.)
• Page Start: 637
• Page End: 659
• Publication Date: 2017-12-13
• Subjects: Image processing -- Numerical approximations and analysis -- Numerical modelling -- Numerical solutions -- Waveform inversion -- Wave propagation; Geophysics -- Periodicals; 550
• DOI: 10.1093/gji/ggx533
• Languages: English
• ISSNs: 0956-540X

Abstract

Summary: 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 3-D case, as compared to classical continuous finite element methods. In this paper, we address this issue in the framework of the so-called hybridizable discontinuous Galerkin (HDG) formulations. As a first step, we study an HDG method for the resolution of the frequency-domain elastic wave equations in the 2-D 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.