Port-Hamiltonian Discontinuous Galerkin Methods for seismic wave computations
Shell/FOM/NWO Computational Science in Energy Research Program 15CSER049
Jaap van der Vegt
We aim to increase the accuracy of seismic wave computations in heterogeneous elastic media that may contain cracks, holes, thin layers and other local structures by developing discontinuous Galerkin (DG) discretizations that preserve the mathematical structure of the (an)isotropic elastic wave equations. To this purpose we combine a DG finite element method with port-Hamiltonian system theory. This mathematical systems approach provides a new framework to derive DG discretizations that have small dispersion and dissipation errors in seismic wave propagation on general unstructured meshes. The discontinuous basis functions in the DG method are also extremely useful for the accurate representation of interfaces with different material properties and to capture important features that are smaller than the dominant seismic wave length, but still affect seismic waves, using hp-adaptive mesh refinement.