The aim of this project is the design, analysis, and implementation of leading edge algorithms for the numerical integration of differential equations arising in mechanics and control applications.

We will consider simulation and modelling of multi-body dynamics, nonholonomic systems, and problems arising in biomedical imaging. Our main scientific goal is to achieve more accurate and reliable numerical simulations of the considered physical phenomena by exploiting the qualitative properties of the underlying models. Our starting point are models with an underlying geometric structure, like for instance differential equations whose solution evolves on a manifold or admits a symmetry. Geometric structure often corresponds to concrete physical features of the model.

We are convinced that the exploitation of this knowledge in a more applied problem setting will lead to significant advance in the considered applications and give new insight for the design of superior numerical strategies.