I work on numerical methods for kinetic equations which provide an intermediate (mesoscopic) description of fluid dynamics that links the microscopic discription by individual particles and the macroscopic description by the Euler or Navier-Stokes equations. To that end, I use a wide range of numerical tools, for instance Galerkin-Petrov methods for the Boltzmann equation that describes the time evolution of a rarefied gas, or Boundary Elements Methods to simulate plasma.

Together with my collegue Andreas Buchheit I have been developing the Singular Euler-Maclaurin method, a tool for the efficient computation of large sums over singular functions that appear in condensed matter physics or quantum mechanics. Our post on the Wolfram Blog gives a concise introduction to our method and discusses the application to a macroscopically large ion chain with 20 billion ions. In collaboration with physicists from the German Aerospace Center we are developing a new understanding of physical systems with long-range interactions.