Junior Research Group: Numerical analysis of multiscale methods
The overall goal of this project is the design and numerical analysis of computational multiscale methods for partial differential equations with general rough and unstructured coefficients and potentially also nonlinearities. Materials with multiscale structures appear in many applications and pose a huge challenge for numerical simulations because fine material features cannot be computationally resolved even with modern computer resources.
Numerical multiscale methods rely on the decomposition of the exact solution into a macroscopic and a fine-scale contribution. Hence, the macroscopic or global behavior of the solution can be faithfully approximated with a coarse mesh.
One special focus of this project is wave propagation in heterogeneous media, which can lead to unusual and astonishing effects such as negative refraction, flat lenses, etc.