Hybridizable Discontinuous Galerkin Methods for modelling 3D seismic wave propagation in harmonic domains

The HPC4E researcher Marie Bonnasse-Gahot (INRIA) presented "Hybridizable Discontinuous Galerkin Methods for modelling 3D seismic wave propagation in harmonic domains" at the 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2017), held at the University of Minnesota (USA). This biannual conference series is one of the main venues for dissemination of the latest advances in theoretical and computational modeling of wave phenomena, catering to the emerging problems in science and technology.

Bonnasse-Gahot presented during the minisymposia, session 6A, "Seismic Waves: Uncertainty Quantification in Imaging/Inversion Across Scales". As explained in the conference website, seismic waves are our primary means of sensing the subsurface of the Earth, at scales that range from a few meters to thousands of kilometers. Determining Earth structure from these waves is challenging because of the inherent nonuniqueness of the inverse problem, as well as the size of the associated computational problem. Because of these challenges, relatively little has been done on the assessment of uncertainty in the inverse problem. A pixel-by-pixel estimate of uncertainty is still computationally intractable, as well as difficult to use as a means to convey uncertainty. This mini-symposium focuses on how we can move toward meaningful measures of uncertainty across all scales of seismic imaging.

In time domain geophysics context, Discontinuous Galerkin (DG) methods are widely studied and used for the simulation of waves propagation. They can be applied to harmonic problems too but their main drawback is that the linear system to solve becomes very huge. Indeed, the number of degrees of freedom is really large as compared to classical finite element methods. We address this issue by considering a new class of DG methods, the hybridizable discontinuous Galerkin (HDG) method. We have formulated and studied the HDG method applied to 2D and 3D elastic waves propagation equations. Then, to be able with realistic 3D geophysical problems, we compare di↵erent solvers, a direct one (Mumps) and an hybrid one (Maphys) that combines direct and iterative solvers by using an algebric domain decomposition method. 

Download the Book of Abstracts from the Conference website (PDF).

Download the presentation (PDF).