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）
Efficient Monte Carlo (MC) sampling of many-body systems with long-range electrostatics is often limited by the cost of per-move energy-difference evaluation under periodic boundary conditions. We present DMK-MC, an accelerated MC method that adapts the dual-space multilevel kernel-splitting (DMK) framework to single-particle Metropolis updates. DMK-MC computes the energy change and, upon acceptance, updates the stored incoming plane-wave fields with $O(1)$ work per tree level, yielding an overall $O(\log N)$ expected work per trial move for fixed accuracy. The method decomposes the Coulomb kernel into three components: a global, periodized smooth part; a multilevel sequence of smooth difference kernels whose interactions are restricted to same-level colleague boxes; and a singular residual kernel whose short-range interactions are evaluated directly. Benchmarks on uniform, highly nonuniform, and implicit-solvent electrolyte and colloidal configurations show that DMK-MC consistently outperforms a recent FMM-based $O(\log N)$ Monte Carlo method, delivering several-fold speedups at comparable tolerances.
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
Infinite Boundary Terms and Pairwise Interactions: A Unified Framework for Periodic Coulomb Systems
Qingdao Institute for Theoretical and Computational Sciences (QiTCS), Center for Optics Research and Engineering, Shandong University（青岛理论计算科学研究所，光学工程研究中心，山东大学）
