The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov–Maxwell equations

We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov–Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge–Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability.