CRC 1114 aims at methodological developments for the modelling and computational simulation of complex processes involving many (more than two) interacting scales, driven by real-life applications from the bio-, geo-, and material sciences. In its individual projects, mathematicians cooperate with colleagues from the natural sciences to advance both their modelling capabilities and their insight into concrete multiscale phenomena.

Job description:
Project C10 within SFB 1114, headed by Prof. Dr. Ana Djurdjevac and Prof. Dr. Nicolas Perkowski, deals with Numerical analysis for nonlinear SPDE models of particle systems. One of the goals of the project is to provide numerical approximations of nonlinear approximations of SPDEs that preserve structure, such as positivity. More specifically, we are studying the Dean-Kawasaki equation.  

The goal of the student research assistant is to assist in investigating finite volume and finite element approximations of SPDEs with divergent noise. We want to investigate also various time integrators. In particular, we are interested in positivity preserving methods and simulations of those methods and comparison with already existing methods. The student's main tasks will be to assist in programming these methods.

Desirable:
- Student of Mathematics
- Programming skills in Matlab or Python
- Knowledge of stochastic analysis, particularly in Markov chains and SDEs
- Knowledge of numerical methods for partial differential equations, in particular finite element methods
- Excellent English language skills (written and spoken, approx. C1)