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

TL;DR

This paper critiques a previous splitting method for the Vlasov-Maxwell equations, clarifying that the incorrect Poisson bracket used previously invalidates the construction of a symplectic scheme.

Contribution

It identifies the error in the previous work's Poisson bracket and explains the implications for symplectic splitting schemes in Vlasov-Maxwell equations.

Findings

The previous Poisson bracket used was incorrect.

Using the correct Poisson bracket prevents exact solution of subsystems.

A symplectic splitting scheme cannot be constructed as previously claimed.

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].