Numerical methods for multiscale problems

The junior research group Numerical Methods for Multiscale Problems, led by Moritz Hauck, is funded by the Collaborative Research Center Wave Phenomena.. Our research focuses on the numerical treatment of multiscale problems, where small-scale effects play an essential role in determining coarse-scale behavior. Such problems arise in a wide range of disciplines, and contexts we are particularly interested in include heterogeneous acoustic and elastic wave propagation problems, flow problems, and diffusion-type processes. Globally resolving all fine-scale features with standard numerical methods is typically prohibitively expensive for multiscale problems, which makes the development of specialized, problem-tailored methods necessary. 

We also investigate multiscale problems in which the heterogeneity is encoded not only in the coefficients but also in the geometry. This includes spatial network models, where the geometry is represented by a graph of edges and nodes, with one-dimensional equations posed on the edges and appropriately coupled at the nodes. A concrete example we consider is the elastic deformation of fiber-based materials, such as paperboard, where Timoshenko beam models are employed as equations on the edges.