After a diploma in pure mathematics I detected the master degree course Computer Simulation in Science. I decided to take part in this study because I wanted to change my focus to an interdisciplinary subject, and this course is a mixture between mathematics, physics and computer science with focus on the computer simulation.

I gained good experience with it: There were only a few students in the class and very kind and helpful lecturers.

During the studies, I liked the compulsory subject Computer Simulation at most, especially the simulation of physical systems. Before, I had no experience with physics and learned a lot thanks to patient lecturers and much work.

Moreover, for me it is impressing that the compulsory subjects enable you to choose one of the quite different elective subjects. For example, I visited lectures in mathematical modelling, theoretical particle and atmospheric physics.

At the end, I wrote an multdisciplinary thesis including numerical mathematics and theoretical particle physics in the subject Mathematical Modelling. This work was very good supervised by a mathematician, Prof. Dr. Michael Günther, as well as a physicist, the CSiS chairman Prof. Dr. Francesco Knechtli.

The title of my master thesis is Implicit partitioned Runge-Kutta integrators for simulations of gauge theories and can be described as follows:

In the simulations of gauge theories, expectation values of certain operators have to be calculated. This is usually performed using a Hybrid Monte Carlo (HMC) method that combines a Metropolis step with a Molecular Dynamics step. During the Molecular Dynamics step, Hamiltonian equations of motion have to be solved through an integration scheme.

Thereby, the integrator has to fulfill the properties time-reversibility and area-preservation. There are state-of-the-art integration methods with these properties, e. g. the Leapfrog scheme as well as splitting methods. At the beginning of this thesis, there was the question if there are any higher order numerical integration schemes for simulations of gauge theories besides the aforementioned methods.

I investigated implicit Runge-Kutta schemes on Lie groups. First of all, I have rewritten the Leapfrog scheme as Runge-Kutta scheme of second order. Afterwards, I focused on higher-order Runge-Kutta methods and developed a time-reversible scheme of order 3. Finally, I implemented a code and performed a HMC simulation using the different integrators.

In the image, the convergence order of the different integration methods can be observed.

After the studies, I started to work in the University of Wuppertal. I have been an employee in the atmospheric physics sector for 1.5 years and changed to the applied mathematics / numerical analysis. At the moment, I write a PhD thesis that proceeds with the work done in the master thesis.