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.