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

Oleksandr Koshkarov (Corresponding author), Gianmarco Manzini, Gian Luca Delzanno (Corresponding author), Cecilia Pagliantini, Vadim Roytershteyn

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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.
Original languageEnglish
Article number107866
Number of pages35
JournalComputer Physics Communications
Publication statusPublished - Jul 2021


  • 3-D Vlasov–Maxwell equations
  • AW Hermite discretization
  • Discontinuous Galerkin method


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