Charge conserving FEM-PIC schemes on general grids

Martin Campos Pinto (1, 2) , Sébastien Jund (1, 2) , Stéphanie Salmon (1, 2) , Eric Sonnendrücker (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 CALVI - Scientific computation and visualization

In this article we aim at proposing a general mathematical formulation for charge conserving finite elements Maxwell solvers coupled with particle schemes. In particular, we identify the finite-element continuity equations that must be satisfied by the discrete current sources for several classes of time domain Vlasov-Maxwell simulations to preserve the Gauss law at each time step, and propose a generic algorithm for computing such consistent sources. Since our results cover a wide range of schemes (namely curl-conforming finite element methods of arbitrary degree, general meshes in 2 or 3 dimensions, several classes of time discretization schemes, particles with arbitrary shape factors and piecewise polynomial trajectories of arbitrary degree), we believe that they provide a useful roadmap in the design of high order charge conserving FEM-PIC numerical schemes.

Mots clés: Maxwell-Vlasov system; conservation of charge; finite element methods; Particle-In-Cell; unstructured grids

Domaines: Analyse numérique [math.NA]

Martin Campos Pinto, Sébastien Jund, Stéphanie Salmon, Eric Sonnendrücker. Charge conserving FEM-PIC schemes on general grids. 2009. ⟨hal-00311429v2⟩