Many physical applications incorporate different scales, for example a microscopic scale where the actual physical process happens and a macroscopic scale where the observable quantity is measured. This scale difference can occur with respect to time in highly oscillating processes over a long time or with respect to space in fine-scale heterogeneous media like composite materials or porous media. In standard computational approaches, the fine scale needs to be resolved everywhere in the heterogeneous medium. Thus, numerical simulations may become extremely costly.

The winter school will address such multiscale problems from an engineering, simulation and mathematical point of view. We will study microscopic modelling, solution methods and concrete applications. We will present analytical homogenisation approaches which yield effective models that separate the micro- and the macroscale and discuss their numerical realization. We will also consider numerical homogenisation methods which are applicable in regimes without a clear scale separation.

Confirmed lecturers:

• Daniel Balzani (Ruhr University Bochum)
• Marc-Andre Keip (University of Stuttgart)
• Mariya Ptashnyk (Heriot-Watt University, Edinburgh)
• Barbara Verfürth (Karlsruhe Institute of Technology)

Format: 12 Lectures, a social event. Participants will have the opportunity to present their own research.

Detailed Schedule: schedule.pdf