SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Wei Guo
Abstract. Understanding behaviors of plasmas plays an increasingly important role in modern science and engineering. A fundamental model in plasma physics is the Vlasov-Maxwell system, which is a nonlinear kinetic transport model describing the dynamics of charged particles due to the self-consistent electromagnetic forces. As predictive simulation tools in studying such complex kinetic system, efficient, reliable and accurate transport schemes are of fundamental significance. The main numerical challenges lies in the high dimensionality, nonlinear coupling, and inherent multi-scale nature in both space and time. In this talk, I will present several numerical methodologies to address these challenges. In this first part, I will introduce a sparse grid discontinuous Galerkin (DG) method for solving the Vlasov equation, which is able to break the curse of dimensionality through a novel sparse approximation space. Meanwhile, attractive properties of DG method are retained. In the second part, an asymptotic preserving Maxwell's solver is developed based on the method of lines transpose approach. The scheme is shown to be able to automatically capture the correct asymptotic limit, known as Darwin model and hence resolve the scale separation issue arising from plasma simulations. Theoretical and numerical results will be represented to demonstrate the efficiency and efficacy of the proposed schemes.