Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations

Abstract

In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. The conservative properties of the algorithm guarantee the efficient and accurate numerical simulation of the Vlasov-Maxwell equations over long-time.

References in corpus (8)

• The serendipity family of finite elements
• Variational formulation of particle algorithms for kinetic plasma simulations
• Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
• Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
• Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov-Maxwell system
• Finite element differential forms on cubical meshes
• A general theory for gauge-free lifting
• Hamiltonian integration methods for Vlasov-Maxwell equations

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