GEMPIC: geometric electromagnetic particle-in-cell methods

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi ident...

Full description

Saved in:
Bibliographic Details
Published in:Journal of plasma physics 2017-08, Vol.83 (4), Article 905830401
Main Authors: Kraus, Michael, Kormann, Katharina, Morrison, Philip J., Sonnendrücker, Eric
Format: Article
Language:English
Subjects:
Atoms & subatomic particles
Calculus
Charged particles
Discretization
Divergence
Electromagnetism
Energy conservation
Finite element method
Hamiltonian functions
Invariants
Magnetic fields
Mathematical analysis
Methods
Numerical analysis
Particle in cell technique
Physics
Plasma physics
Splitting
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss’ law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.
ISSN:0022-3778
1469-7807
DOI:10.1017/S002237781700040X