Hamiltonian integration methods for Vlasov-Maxwell equations

Abstract

Hamiltonian integration methods for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, i.e., the electrical energy, the magnetic energy, and the kinetic energy in three Cartesian components. Each of the subsystems is a Hamiltonian system with respect to the Morrison-Marsden-Weinstein Poisson bracket and can be solved exactly. Compositions of the exact solutions yield Poisson structure preserving, or Hamiltonian, integration methods for the Vlasov-Maxwell equations, which have superior long-term fidelity and accuracy.

References in corpus (5)

• 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
• Variational integration for ideal magnetohydrodynamics with built-in advection equations
• Energetically-consistent collisional gyrokinetics
• Comment on "Hamiltonian splitting for the Vlasov-Maxwell equations"

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