Energy-conserving time propagation for a structure-preserving particle-in-cell Vlasov–Maxwell solver
Katharina Kormann, Eric Sonnendrücker
Abstract
Abstract 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 a splitting that yields constant Poisson matrices in each substep. 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.
BibTeX
@article{Kormann_2021,
title={Energy-conserving time propagation for a structure-preserving particle-in-cell Vlasov–Maxwell solver},
volume={425},
ISSN={0021-9991},
url={http://dx.doi.org/10.1016/j.jcp.2020.109890},
DOI={10.1016/j.jcp.2020.109890},
journal={Journal of Computational Physics},
publisher={Elsevier BV},
author={Kormann, Katharina and Sonnendrücker, Eric},
year={2021},
month=jan,
pages={109890} }