Comment on "Hamiltonian splitting for the Vlasov-Maxwell equations"

Abstract

The paper [1] by Crouseilles, Einkemmer, and Faou used an incorrect Poisson bracket for the Vlasov-Maxwell equations. If the correct Poisson bracket is used, the solution of one of the subsystems cannot be computed exactly in general. As a result, one cannot construct a symplectic scheme for the Vlasov-Maxwell equations using the splitting Hamiltonian method proposed in Ref [1].

6 pages

References in corpus (1)

• A general theory for gauge-free lifting

Cited by in corpus (16)

• GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
• Structure and structure-preserving algorithms for plasma physics
• Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
• Structure-Preserving Geometric Particle-in-Cell Methods for Vlasov-Maxwell Systems
• Explicit symplectic algorithms based on generating functions for charged particle dynamics
• Hamiltonian integration methods for Vlasov-Maxwell equations
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• Explicit Structure-Preserving Geometric Particle-in-Cell Algorithm in Curvilinear Orthogonal Coordinate Systems and Its Applications to Whole-Device 6D Kinetic Simulations of Tokamak Physics
• Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics
• Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field
• Local Energy Conservation Law for Spatially-Discretized Hamiltonian Vlasov-Maxwell System
• An asymptotic preserving scheme for the relativistic Vlasov--Maxwell equations in the classical limit
• A dual grid geometric electromagnetic particle in cell method
• A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus
• Splitting methods for Fourier spectral discretizations of the strongly magnetized Vlasov-Poisson and the Vlasov-Maxwell system
• Symplectic particle-in-cell methods for hybrid plasma models with Boltzmann electrons and space-charge effects