Solving the Vlasov–Maxwell equations using Hamiltonian splitting

•Our Hamiltonian splitting method preserves Poisson structure of Vlasov–Maxwell system.•The Gauss's Law is satisfied by the solution after time discretization.•The evolution of distribution function can be expressed as several one-dimensional translations. In this paper, the numerical discretizations based on Hamiltonian splitting for solving the Vlasov–Maxwell system are constructed. We reformulate the Vlasov–Maxwell system in Morrison–Marsden–Weinstein Poisson bracket form. Then the Hamiltonian of this system is split into five parts, with which five corresponding Hamiltonian subsystems are obtained. The splitting method in time is derived by composing the solutions to these five subsystems. Combining the splitting method in time with the Fourier spectral method and finite volume method in space gives the full numerical discretizations which possess good conservation for the conserved quantities including energy, momentum, charge, etc. In numerical experiments, we simulate the Landau damping, Weibel instability and Bernstein wave to verify the numerical algorithms.