One of the fundamental questions is: What is the world made of and what holds it together? (further reading) For this purpose, the properties of elementary particles (hadrons) are investigated using computer simulations. These theoretical results are needed to analyze some experiments as, for example, done at the Large Hadron Collider LHC at the CERN.

Strong forces are responsible for the binding of quarks and gluons to make e. g. protons and neutrons. The theory of strong interaction is called Quantum Chromodynamics (QCD). (further reading)

Computer simulations in QCD are based on the discretization of the theory on an Euklidean lattice. Here equations of motion, defined either via classical equations of motion (Hybrid Monte Carlo) or stochastic differential equations, have to be solved numerically. In both cases, the time integration has to be done in a non-abelian Lie group and causes a high computational effort. Moreover, these integration methods must be symmetric and symplectic to reflect realistic physical situations.

In our group, we investigate and enhance geometric numerical integration methods for differential equations in Lie groups. To speed up simulations and allow for larger lattices, we develop high-order implicit partitioned Runge-Kutta integrators and combine them with multirate schemes.