Hamiltonian integration methods for Vlasov-Maxwell equations

TL;DR

This paper develops Hamiltonian splitting methods for the Vlasov-Maxwell equations, enabling exact solutions of subsystems and resulting in structure-preserving integrators with improved long-term accuracy.

Contribution

It introduces a novel Hamiltonian splitting approach that preserves the Poisson structure for Vlasov-Maxwell equations, enhancing numerical fidelity.

Findings

The methods preserve the Hamiltonian structure over long simulations.

Exact solutions of subsystems improve numerical stability.

The integrators demonstrate superior accuracy in tests.

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.