Extending the Numerical Flow Iteration to the multi-species Vlasov-Maxwell system through Hamiltonian Splitting

TL;DR

This paper extends the memory-efficient Numerical Flow Iteration (NuFI) method from the Vlasov-Poisson system to the more complex Vlasov-Maxwell system, maintaining its structure-preserving and high-fidelity properties.

Contribution

It introduces a Hamiltonian splitting approach to adapt NuFI for electromagnetic plasma dynamics, preserving its accuracy and low-memory advantages.

Findings

NuFI can be extended to the Vlasov-Maxwell system without losing structure-preserving properties.

The extended NuFI maintains high accuracy and low memory usage in electromagnetic plasma simulations.

The method effectively handles the full electromagnetic kinetic plasma dynamics.

Abstract

The Numerical Flow Iteration (NuFI) method has recently been proposed as a memory-slim solution method for the Vlasov--Poisson system. It stores the temporal evolution of the electric field, instead of the distribution functions, and reconstructs the solution in each time step by following the characteristics backwards in time and reconstructing the solution from the initial distribution. NuFI has been shown to be more accurate than other state-of-the-art Vlasov solvers given the same amount of degrees of freedom as well as interpolation order, essentially making NuFI a high-fidelity but low-memory cost scheme. In this paper, we build on the Hamiltonian structure of the full Vlasov--Maxwell system to extend NuFI to handle electro-magnetic kinetic plasma dynamics. We show that the advanced structure-preserving properties of NuFI are preserved when extending to the electro-magnetic case.