The focus of the group is on research and application with regard to mathematical modelling and numerical simulation in metrology. Main themes comprise:
- Mathematical modelling of physical processes and measurement setups
- Numerical simulations of measurement processes and virtual experiments
- Solution of inverse problems for parameter identification from measurement data
- Model-based optimization of measurements
A common thread is the treatment of partial differential equations (PDEs), which are employed to model stationary states and dynamical processes. Methods encompass application of a broad variety of discretization schemes, e. g. finite differences, finite elements and spectral methods as well as methods for the solution of deterministic and statistic inverse problems and the analysis of the behavior of nonlinear PDEs. A recent topic are methods for uncertainty quantification regarding results in PDEs with uncertain input parameters, e.g. with the help of smart sampling methods or surrogate models.
Main application areas are:
- Modelling of electromagnetic fields and inverse problems in optics, nanometrology and medical physics
- Simulations of macroscopic flows and transport processes
- Modelling of active biological fluids
Until the end of 2015 further topics in particular numerical heart modelling, coupled oscillators, control of self-organised structures and dynamics of active particles were investigated, which have now become the topics of the newly founded working group 8.43 „Complex systems in biophysics and medicine“. The topic of pattern formation in chemical and biological reaction-diffusion systems has been pursued until 2014 and is currently not under active investigation.