Hybridizable Discontinuous Galerkin Methods for Solving Helmholtz Equations

As the drilling is expensive, the petroleum industry is interested by methods able to produce images of the intern sturctures of the Earth before the drilling. Seismic imaging can be processed in time-domain or in harmonic-domain. The imaging condition is easier to obtain in frequency domain, but solving the Helmholtz equations in 3D is almost impossible due to a huge computationnal cost, even with the help of High Performance Computing. We then have to develop less expensive methods. We consider hybridizable discontinuous Galerkin (HDG) method to solve Helmholtz equations : because it is a discontinuous Galerkin method, it is more convenient to handle the topography of the subsurface than finite difference methods and we can use unstructured meshes and have a flexible choice of interpolation orders. Moreover, as it is an hybrid method we reduce the globally coupled unknowns leading to a reduction of the computational cost.