A general framework for structure-preserving particle approximations to Vlasov-Maxwell equations
Variational discretizations are known for preserving key physical invariants in a natural way, leading to long-time stability properties. In this talk I will present a discrete action principle for the Vlasov-Maxwell equations that applies in a general structure-preserving discrete framework.
In this framework the finite-dimensional electromagnetic potentials and fields are represented in a discrete de Rham sequence involving general Finite Element spaces, and the particle-field coupling is represented by a set of projection operators that commute with the differential operators.
One application of this approach is a new variational spectral PIC method that has a discrete Hamiltonian structure and relies on particle-field coupling techniques very similar to those encountered in standard PIC schemes.
This is a joint work with Jakob Ameres, Katharina Kormann and Eric Sonnendrücker from the Max Planck IPP in Garching, Germany