DOWNLOAD PRESENTATIONWATCH VIDEOIn the most widely used methods for seismic imaging, we have to solve 2N wave equations at each iteration of the selected process if N sources are used. N is usually large and the efficiency of the whole simulation algorithm is directly related to the efficiency of the numerical method used to solve the wave equations.
Seismic imaging can be performed in time domain but there is an advantage in considering frequency domain. It is indeed not necessary to store the solution at each time step of the forward simulation. The main drawback lies then in solving large linear systems, which represents a challenging task when considering realistic 3D elastic media, despite the recent advances on high performance numerical solvers. In this context, the goal of our study is to develop new solvers based on reduced-size matrices without hampering the accuracy of the numerical solution.
We consider Discontinuous Galerkin methods (DGm) which are more convenient than finite difference methods to handle the topography of the subsurface. DGm and classical Finite Element methods (Fem) mainly differ from discrete functions which are only piecewise continuous in the case of DGm. DGm are then suitable to deal with hp-adaptivity. This is a great advantage to DGm which is thus fully adapted to calculations in highly heterogeneous media. The main drawback of classical DGm is that they are more expensive in terms of number of unknowns than classical FEm.
In this work we consider a hybridizable DG method (HDGm). Its principle consists in introducing a Lagrange multiplier representing the trace of the numerical solution on each face of the mesh cells. This new variable exists only on the faces and the unknowns of the problem depend on it. This allows us to reduce the number of unknowns of the global linear system. The solution to the initial problem is then recovered thanks to independent elementwise calculation. The parallelization of the HDG formulation does not induce any additional difficulty in comparison with classical DGm.
We have compared the performance of the HDG method with the one of nodal DGm for the 2D elastic waves propagation in harmonic domain. Preliminary results show that HDGm is better than DGm both for computational time and matrix storage. We are performing scalability-tests (strong and weak) in order to study the performance portability and the HPC efficiency.
This work is a preliminary work before considering the more general 3D case.
