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Title: GEMPIC: geometric electromagnetic particle-in-cell methods

Abstract

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.

Authors:
ORCiD logo; ; ;
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1534399
DOE Contract Number:  
FG05-80ET53088
Resource Type:
Journal Article
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 83; Journal Issue: 4; Journal ID: ISSN 0022-3778
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
Physics

Citation Formats

Kraus, Michael, Kormann, Katharina, Morrison, Philip J., and Sonnendrücker, Eric. GEMPIC: geometric electromagnetic particle-in-cell methods. United States: N. p., 2017. Web. doi:10.1017/s002237781700040x.
Kraus, Michael, Kormann, Katharina, Morrison, Philip J., & Sonnendrücker, Eric. GEMPIC: geometric electromagnetic particle-in-cell methods. United States. doi:10.1017/s002237781700040x.
Kraus, Michael, Kormann, Katharina, Morrison, Philip J., and Sonnendrücker, Eric. Mon . "GEMPIC: geometric electromagnetic particle-in-cell methods". United States. doi:10.1017/s002237781700040x.
@article{osti_1534399,
title = {GEMPIC: geometric electromagnetic particle-in-cell methods},
author = {Kraus, Michael and Kormann, Katharina and Morrison, Philip J. and Sonnendrücker, Eric},
abstractNote = {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.},
doi = {10.1017/s002237781700040x},
journal = {Journal of Plasma Physics},
issn = {0022-3778},
number = 4,
volume = 83,
place = {United States},
year = {2017},
month = {7}
}

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