To avoid ineffective collisions between the equilibrium states, the hybrid method with deviational particles (HDP) has been proposed to integrate the Fokker-Planck-Landau system, while leaving a new issue in sampling deviational particles from the high-dimensional source term. In this paper, we present an adaptive sampling (AS) strategy that first adaptively reconstructs a piecewise constant approximation of the source term based on sequential clustering via discrepancy estimation, and then samples deviational particles directly from the resulting adaptive piecewise constant function without rejection. The mixture discrepancy, which can be easily calculated thanks to its explicit analytical expression, is employed as a measure of uniformity instead of the star discrepancy the calculation of which is NP-hard. The resulting method, dubbed the HDP-AS method, runs approximately ten times faster than the HDP method while keeping the same accuracy in the Landau damping, two stream instability, bump on tail and Rosenbluth's test problem.

翻译：为避免平衡态间的无效碰撞，已提出采用偏差粒子的混合方法（HDP）来求解Fokker-Planck-Landau系统，但该方法在从高维源项采样偏差粒子时产生了新问题。本文提出一种自适应采样（AS）策略：首先基于通过差异度估计的序列聚类，自适应地重构源项的分段常数近似；随后直接从所得的自适应分段常数函数中采样偏差粒子而无需拒绝操作。得益于其显式解析表达式可轻松计算的混合差异度，被用作均匀性度量指标，替代了计算复杂度为NP难的星形差异度。所得方法称为HDP-AS方法，在Landau阻尼、双流不稳定性、尾峰问题和Rosenbluth测试算例中，在保持相同精度的前提下，其运行速度较HDP方法提升约十倍。