The realistic simulation of wave propagation phenomena requires several steps, starting with the choice of the partial differential equation model, its analysis, the development of stable numerical methods for it and their efficient implementation. I will give three separate examples related to research projects at KIT to illustrate my field of work:

•     The construction of reliable Perfectly Matched Layer (PML) methods for anisotropic equations to enable seismological simulations in anisotropic rock layers.
•     The development of stable finite element methods (FEM) for transmission eigenvalue problems in dispersive materials to calculate plasmonic resonances of nanostructures.
•     The modeling of coupled nonlinear acoustic problems, e.g. for ultrasonic applications.