Direct simulation Monte Carlo schemes for Coulomb interactions in plasmas
Université de Toulouse（图卢兹大学；UPS，INSA，UT1，UTM；图卢兹数学研究所）；UPS, INSA, UT1, UTM（加州大学洛杉矶分校数学系）；Institut de Mathématiques de Toulouse（费拉拉大学数学系和CMCS）；Mathematics Department, University of California, Los Angeles (UCLA)；Mathematics Department and CMCS, University of Ferrara
Giacomo Dimarco, Russell Caflisch, Lorenzo Pareschi
发表信息：
Communications in Applied and Industrial Mathematics 2010
我们考虑开发用于具有库仑相互作用的分子系统的蒙特卡罗方案。借助Bobylev和Nanbu引入的近似（气体和等离子体碰撞算法的理论，基于玻尔兹曼方程和Landau-Fokker-Planck方程，Physical Review E, Vol. 61, 2000），我们将Bird和Nanbu-Babovsky的经典稀薄气体动力学算法推广到库仑情况。因此，方案不是基于原始的玻尔兹曼碰撞算子，而是通过使用近似的玻尔兹曼算子构建。上述选择允许在模拟中使用更大的时间步长；此外，避免了昂贵的接受-拒绝碰撞过程，并且每个粒子都参与碰撞。进行了误差分析以及与原始Bobylev-Nanbu (BN)方案的比较。数值结果显示，近似玻尔兹曼算子的理论收敛速率与数值结果一致，并且Bird型方案相对于原始方案具有更好的性能。
英文摘要：
We consider the development of Monte Carlo schemes for molecules with Coulomb interactions. We generalize the classic algorithms of Bird and Nanbu-Babovsky for rarefied gas dynamics to the Coulomb case thanks to the approximation introduced by Bobylev and Nanbu (Theory of collision algorithms for gases and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation, Physical Review E, Vol. 61, 2000). Thus, instead of considering the original Boltzmann collision operator, the schemes are constructed through the use of an approximated Boltzmann operator. With the above choice larger time steps are possible in simulations; moreover the expensive acceptance-rejection procedure for collisions is avoided and every particle collides. Error analysis and comparisons with the original Bobylev-Nanbu (BN) scheme are performed. The numerical results show agreement with the theoretical convergence rate of the approximated Boltzmann operator and the better performance of Bird-type schemes with respect to the original scheme.
Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes
本文为等离子体动力学模型中库仑碰撞的离散化提供了新的见解。基于以前的工作[Carrillo et al. J. Comp. Phys. X 7：100066（2020），Hirvijoki and Burby Phys. Plasmas 27（8）：082307（2020）]，我提出了标准Landau碰撞算子和静电回旋Landau算子的确定性离散时间能量和正性保持，熵耗散标记粒子方案。在标准朗道算子的情况下，该方案还保留了离散时间的动力学动量。这些改进，[Carrillo et al. J. Comp. Phys. X 7：100066（2020），Hirvijoki and Burby Phys. Plasmas 27（8）：082307（2020）]中的结构保持离散化到离散时间的扩展，通过利用所涉及的碰撞算子和所谓的离散梯度积分器的底层metriplectic结构而成为可能。
Implicit and electrostatic Particle-in-cell/Monte Carlo model in two dimensional and axisymmetric geometry II: Self-bias voltage effects in capacitively coupled plasmas
An $O(\log N)$ Monte Carlo method for periodic Coulomb systems
Center for Computational Mathematics, Flatiron Institute, Simons Foundation（西蒙斯基金会平顿研究所计算数学中心）；School of Mathematical Sciences, MOE-LSC and CMA-Shanghai, Shanghai Jiao Tong University（上海交通大学数学科学学院，教育部重点实验室与上海计算数学与应用数学研究院）
