Modeling and numerical simulation of wave propagation phenomena

Abstract

Realistic simulations of wave propagation phenomena require several steps, beginning with the selection of the partial differential equation model, its analysis, the development of stable numerical methods for this purpose, and their efficient implementation. I will present three separate examples related to research projects at KIT, in which I will introduce my field of work:
1) The construction of reliable Perfectly Matched Layer (PML) methods for anisotropic equations, to enable seismological simulations in anisotropic rock layers.
2) The development of stable finite element methods (FEM) for transmission eigenvalue problems in dispersive materials to calculate plasmonic resonances of nanostructures.
3) The modeling of coupled nonlinear acoustic problems, e.g., for ultrasound applications.