Past Event: Oden Institute Seminar

Geometric electromagnetic PIC models

Eric Sonnendrücker , Professor, Director of Numerical Methods in Plasma Physics Division, Max Planck Institute for Plasma Physics, Germany

Abstract

A hamiltonian framework for the derivation of semi-discrete (continuous in time) Finite Element Particle In Cell approximations of the Vlasov-Maxwell equations was derived in [1]. It is based on a particle (Klimontovitch) discretization of the distribution function and a compatible Finite Element discretization of the grid quantities. The ideas introduced in [1]can be declined in dierent variants, choosing dierent discrete spaces for the elds or adding smoothing functions for the particles. Moreover, starting from such a semi-discretization, which yields a finite dimensional Hamiltonian structure defined by a Poisson J (U) matrix and a hamiltonian H(U), several classes of dierent structure preserving time discretization can be derived: hamiltonian splitting methods as in [1], that preserve the Poisson structure, or discrete gradient methods that preserve exactly the hamiltonian. This procedure enables in particular to recover and generalize several well-known explicit and implicit PIC algorithms. We are going in this talk to give an overview of the geometric ideas behind this structure and how they can be used to derive fully discrete particle in cell schemes with exact conservation of the Poisson structure, the energy and Gauss' law. References [1] M. Kraus, K. Kormann, P.J. Morrison, E. Sonnendrucker. GEMPIC: Geometric electromagnetic particle-in-cell methods. Journal of Plasma Physics,83(4), (2017).