The Numerical Mathematics department develops efficient modelling, simulation, and optimization tools and algorithms for challenging application problems from medicine, systems biology, and molecular dynamics as well as nano-optical systems and humanities. Based on tight collaboration with application partners, the department aims not only at generating scientific insight, but also at providing software prototypes and demonstrators for specific solutions.

For these, we develop adaptive algorithms in the areas of finite elements, agent-based models, conformation dynamics, optimal control,  and parameter estimation, exploiting multi-level structures for efficiency and robustness. With increasing complexity of the applications, techniques for multi-scale, multi-physics and hybrid models play a more and more important role, as do stochastic aspects, uncertainty quantification, and design tasks.