Discontinuous Galerkin pseudospectral time domain algorithm (DG-PSTD) with auxiliary ordinary differential equations perfectly matched layer (AODE-PML) for 3D seismic modelling

A discontinuous Galerkin pseudospectral time domain (DGPSTD) algorithm is proposed for the elastic wave propagation problem in unbounded domains, where an equivalent but significantly simpler auxiliary ordinary differential equations (AODEs) formulation of 3D perfectly matched layer (PML) is used to truncate the computational domain. A more accurate Riemann solver, i.e., the Godunov flux is provided to not only resolve the coupling of subdomains but also give an explicit guideline for the new governing equations in the PML region. The proposed DGPSTD algorithm combines the merits of flexibility from a finite element method and spectral accuracy and efficiency from a high-order pseudospectral method while having a flavor closer to a finite volume method. Test results show that the newly proposed AODE-PML needs only oneelement PML layer to absorb outgoing waves efficiently and sufficiently.