ADER-DG - Analysis, further Development and Applications

After introducing the Discontinuous Galerkin (DG) method a detailed misfit analysis on its numerical approximation is performed. We investigate the accuracy of the scheme, the element type (tetrahedrons and hexahedrons), the spatial sampling of the computational domain and the number of propagated wavelengths. As the error norm we chose a time-frequency representation, which illustrates the time evolution of the spectral content. The results of this analysis are confirmed by a multi-institutional code validation project. In order to improve efficiency, we expand the computer code to non-conforming, hybrid meshes. In 2 dimensions, riangulars and quadrilaterals can be combined within one computational domain. Several convergence tests are carried out and the newly invented scheme is applied to different test cases including thin layers and variable material. Furthermore, as absorbing boundaries suffer from spurious reflections at artificial boundaries of the computational domain, we introduce a convolutional perfectly matched layer (CPML) to the scheme. Due to the loss of definite stability, we accomplish several test cases in order to examine the scheme’s behavior. A switchoff criterion for the CPML is suggested. Considering topographic effects on seismic waves, we perform a systematic study of different parameterizations involving the wave type and frequency of the input signal, the dataset resolution and various amplification factors of real topography in the region of Grenoble, France. Special events are simulated at Mt. Hochstaufen, Southern Bavaria, and compared to real recordings.