Aurelien Citrain defended his PhD thesis entitled:
Hybrid finite element methods for seismic wave simulation: coupling of
Discontinuous Galerkin and Spectral Element discretizations
To solve wave equations in heterogeneous media with finite elements with
a reasonable numerical cost, we couple the Discontinuous Galerkin method (DGm) with
Spectral Elements method (SEm). We use hybrid meshes composed of tetrahedra and
structured hexahedra. The coupling is carried out starting from a mixed-primal DG
formulation applied on a hybrid mesh composed of a hexahedral macro-element and a
sub-mesh composed of tetrahedra. The SEm is applied in the macro-element paved with
structured hexahedrons and the coupling is ensured by the DGm numerical fluxes applied
on the internal faces of the macro-element common with the tetrahedral mesh. The sta-
bility of the coupled method is demonstrated when time integration is performed with a
Leap-Frog scheme. The performance of the coupled method is studied numerically and it
is shown that the coupling reduces numerical costs while keeping a high level of accuracy.
It is also shown that the coupled formulation can stabilize the DGm applied in areas that
include Perfectly Matched Layers.
Pau, December 16, 2019
