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Variational Framework for Structure-Preserving Electromagnetic Particle-in-Cell Methods
Max Planck Inst Plasma Phys, Garching, Germany..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science. Max Planck Inst Plasma Phys, Garching, Germany.;Tech Univ Munich, Zentrum Math, Garching, Germany..
Max Planck Inst Plasma Phys, Garching, Germany.;Tech Univ Munich, Zentrum Math, Garching, Germany..
2022 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 91, no 2, article id 46Article in journal (Refereed) Published
Abstract [en]

In this article we apply a discrete action principle for the Vlasov-Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are represented in a discrete de Rham sequence involving general finite element spaces, and the particle-field coupling is represented by a set of projection operators that commute with the differential operators. With a minimal number of assumptions which allow for a variety of finite elements and shape functions for the particles, we show that the resulting variational scheme has a general discrete Poisson structure and thus leads to a semi-discrete Hamiltonian system. By introducing discrete interior products we derive a second type of space discretization which is momentum preserving, based on the same finite elements and shape functions. We illustrate our method by applying it to spline finite elements, and to a new spectral discretization where the particle-field coupling relies on discrete Fourier transforms.

Place, publisher, year, edition, pages
Springer Nature Springer Nature, 2022. Vol. 91, no 2, article id 46
Keywords [en]
Vlasov-Maxwell, Particle-in-cell, Variational methods, Hamiltonian structure, Structure-preserving finite elements, Commuting de Rham diagram
National Category
Computational Mathematics
Research subject
Scientific Computing
Identifiers
URN: urn:nbn:se:uu:diva-472745DOI: 10.1007/s10915-022-01781-3ISI: 000776724800002OAI: oai:DiVA.org:uu-472745DiVA, id: diva2:1652620
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eSSENCE - An eScience CollaborationAvailable from: 2022-04-19 Created: 2022-04-19 Last updated: 2024-01-15Bibliographically approved

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Kormann, Katharina

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