Invited Lecture
Structure preserving semi-Lagrangian discontinuous Galerkin methods for kinetic plasma simulation
University of Innsbruck, Austria,
Abstract
In this talk, we consider collisionless kinetic models from plasma physics such as the Vlasov equation or the drift-kinetic equation. Since those equations are posed in an up to six-dimensional phase space, their numerical solution can be extremely challenging. Thus, efficient numerical methods are vital. Semi-Lagrangian methods are commonly used, but most such state of the art methods rely on global methods such as cubic splines or spectral approaches. In addition, a numerical scheme is sought that does not introduce too much numerical diffusion while still being conservative. We propose a splitting based semi-Lagrangian discontinuous Galerkin (SLDG) approach that is both completely local and explicit and has less numerical diffusion compared to cubic splines. These methods can, as we demonstrate, be effectively used on supercomputers with thousands of GPUs. We also discuss recent advances in solving more complicated problems that require a two-dimensional interpolation and discuss limiting for such methods.