Multi-scale differential equation models from physics, chemistry and biology place high demands on analysis simulation. Due to a multitude of state variables and parameters, a dimensional reduction of the models can be helpful. For this purpose we develop analytical and numerical methods. Interdisciplinary idea transfer, e.g. from classical mechanics in variable Lagrange-Hamilton-Jacobi form, statistical physics and relativity theory, plays a central role.

We apply coordinate independent, differential geometric and function theoretical methods for the analytical and numerical characterization of phase space geometry and topology of dynamic systems (ordinary and parabolic partial differential equations). In particular, geometric approaches for model reduction and approximation of dynamic systems are developed and tools for complex analysis are made available through analytical continuations.

Optimization and optimum control of process sequences play an important role in flow-through reactors in chemistry and biotechnology, for example. We use powerful numerical methods based on theory, especially with regard to robustness and efficiency. We also use model reduction and real-time algorithms (collaboration with working group of Prof. Moritz Diehl, IMTEK Freiburg), which are used in the field of control engineering for autonomous driving and wind power generation.