We study a grid-free particle method based on following the evolution of the characteristics of the Vlasov–Poisson system, and we show that it converges for smooth enough initial data. This method is built as a combination of well-studied building blocks—mainly time integration and integral quadratures—and allows to obtain arbitrarily high orders. By making use of the Non-Uniform Fast Fourier Transform, the overall computational complexity is \( {\mathcal {O}}(P \log P + K^d \log K^d) \), where \( P \) is the total number of particles and where we only keep the Fourier modes \( k \in ({\mathbb {Z}}^d)^* \) such that \( k_1^2 + \dots + k_d^2 \le K^2 \). Some numerical results are given for the Vlasov–Poisson system in the one-dimensional case.

我们研究了一种基于遵循 Vlasov-Poisson 系统特征演化的无网格粒子方法，并证明它可以收敛到足够光滑的初始数据。该方法是作为经过充分研究的构建块（主要是时间积分和积分求积）的组合而构建的，并且允许获得任意高阶。通过使用非均匀快速傅立叶变换，整体计算复杂度为\( {\mathcal {O}}(P \log P + K^d \log K^d) \)，其中\( P \)是粒子总数，我们只保留傅里叶模式\( k \in ({\mathbb {Z}}^d)^* \)使得\( k_1^2 + \dots + k_d^2 \le K^2 \)。给出了一维情况下 Vlasov-Poisson 系统的一些数值结果。