Non-conforming hybrid meshes for efficient 2D wave propagation using the Discontinuous Galerkin method

We present a Discontinuous Galerkin finite element method using a high-order time integration technique for seismic wave propagation modelling on non-conforming hybrid meshes in two space dimensions. The scheme can be formulated to achieve the same approximation order in space and time and avoids numerical artifacts due to non-conforming mesh transitions or the change of the element type. A point-wise Gaussian integration along partially overlapping edges of adjacent elements is used to preserve the schemes accuracy while providing a higher flexibility in the problem-adapted mesh generation process. We describe the domain decomposition strategy of the parallel implementation and validate the performance of the new scheme by numerical convergence test and experiments with comparisons to independent reference solutions. The advantage of non-conforming hybrid meshes is the possibility to choose the mesh spacing proportional to the seismic velocity structure, that allows for simple refinement or coarsening methods even for regular quadrilateral meshes. For particular problems of strong material contrasts and geometrically thin structures the scheme reduces the computational cost in the sense of memory and run-time requirements. The presented results promise to achieve the same behavior for an extension to three space dimensions were the coupling of tetrahedral and hexahedral elements necessitates non-conforming mesh transitions in order to avoid linking elements in form of pyramids.

@article{id1430,
  author = {Hermann, Verena and K\"aser, Martin and Castro, E. Cristobal},
  doi = {10.1111/j.1365-246X.2010.04858.x},
  journal = {Geophys. J. Int.},
  language = {en},
  number = {2},
  pages = {746-758},
  title = {Non-conforming hybrid meshes for efficient 2D wave propagation using the Discontinuous Galerkin method},
  volume = {184},
  year = {2011},
}

%O Journal Article
%A Hermann, Verena
%A Käser, Martin
%A Castro, E. Cristobal
%R 10.1111/j.1365-246X.2010.04858.x
%J Geophys. J. Int.
%G en
%N 2
%P 746-758
%T Non-conforming hybrid meshes for efficient 2D wave propagation using the Discontinuous Galerkin method
%V 184
%D 2011