Energy-conserving time propagation for a geometric particle-in-cell Vlasov–Maxwell solver

10/09/2019

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by   Katharina Kormann, et al.

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This paper discusses energy-conserving time-discretizations for finite element particle-in-cell discretizations of the Vlasov–Maxwell system. A geometric spatially discrete system can be obtained using a standard particle-in-cell discretization of the particle distribution and compatible finite element spaces for the fields to discretize the Poisson bracket of the Vlasov–Maxwell model (see Kraus et al., J Plasma Phys 83, 2017). In this paper, we derive energy-conserving time-discretizations based on the discrete gradient method applied to an antisymmetric splitting of the Poisson matrix. Firstly, we propose a semi-implicit method based on the average-vector-field discretization of the subsystems. Moreover, we devise an alternative discrete gradient that yields a time discretization that can additionally conserve Gauss' law. Finally, we explain how substepping for fast species dynamics can be incorporated.