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.

我们讨论了用于三维Vlasov-Maxwell方程数值模拟的频谱方法的开发，分析，实现和数值评估。该方法基于具有不对称加权Hermite函数的速度空间的频谱扩展。通过使用不连续的Galerkin（DG）方法在空间中以及通过使用显式Runge-Kutta积分器进行时间积分的线法，可以离散化所得的时间相关非线性方程组。生成的代码称为“光谱等离子解算器（SPS-DG）”，已成功应用于标准等离子物理基准测试，以证明其准确性，鲁棒性和并行可扩展性。