A Dual Grid Geometric Electromagnetic Particle in Cell Method
Abstract.
Geometric particle-in-cell discretizations have been derived based on a discretization of the fields that is conforming with the de Rham structure of the Maxwell’s equations and a standard particle-in-cell ansatz for the fields by deriving the equations of motion from a discrete action principle. While earlier work has focused on finite-element discretization of the fields based on the theory of finite-element exterior calculus, we propose in this article an alternative formulation of the field equations that is based on the ideas conveyed by mimetic finite differences, the needed duality being expressed by the use of staggered grids. We construct a finite-difference formulation based on degrees of freedom defined as point values, edge, face, and volume integrals on a primal and its dual grid. Compared to the finite-element formulation, no mass matrix inversion is involved in the formulation of the Maxwell solver. In numerical experiments, we verify the conservation properties of the novel method and study the influence of the various parameters in the discretization.
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Acknowledgments.
We would like to thank Martin Campos Pinto for valuable discussions and all the contributors to the GEMPICX code.
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Information & Authors
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Published In
SIAM Journal on Scientific Computing
Pages: B621 - B646
DOI: 10.1137/23M1618910
ISSN (online): 1095-7197
Copyright
© 2024 Society for Industrial and Applied Mathematics.
History
Submitted: 13 December 2023
Accepted: 26 June 2024
Published online: 4 October 2024
Keywords
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Funding Information
H2020 Euratom (EURATOM): 101052200
Funding: This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (grant agreement 101052200, EUROfusion). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. The first author acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center SFB1491 Cosmic Interacting Matters—From Source to Signal.
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- A geometric Particle-In-Cell discretization of the drift-kinetic and fully kinetic Vlasov–Maxwell equationsPlasma Physics and Controlled Fusion, Vol. 67, No. 5 | 14 April 2025
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