We present a novel family of particle discretisation methods for the nonlinear Landau collision operator. We exploit the metriplectic structure underlying the Vlasov-Maxwell-Landau system in order to obtain disretisation schemes that automatically preserve mass, momentum, and energy, warrant monotonic dissipation of entropy, and are thus guaranteed to respect the laws of thermodynamics. In contrast to recent works that used radial basis functions and similar methods for regularisation, here we use an auxiliary spline or finite element representation of the distribution function to this end. Discrete gradient methods are employed to guarantee the aforementioned properties in the time discrete domain as well.

翻译：我们提出了一类用于非线性朗道碰撞算子的新型粒子离散方法。通过利用Vlasov-Maxwell-Landau系统底层度量辛结构，我们构建了可自动保持质量、动量与能量守恒、确保熵单调耗散的离散格式，从而严格遵循热力学定律。与近期采用径向基函数及类似正则化技术的研究不同，本文通过引入辅助样条或有限元分布函数表示来实现上述目标。此外，我们采用离散梯度方法以保证时间离散域中同样具备所述特性。