主讲人：杜恺 复旦大学副教授
时间：2025年9月4日10：30
地点：三号楼332室
举办单位：数理学院
主讲人介绍：杜恺，复旦大学上海数学中心长聘副教授、博士生导师。2011年获复旦大学博士学位，曾任职于苏黎世联邦理工学院 (ETH)、澳大利亚 Wollongong 大学。主要研究方向包括随机分析、偏微分方程、最优控制、强化学习等，成果发表于 PTRF、TAMS、SICON、JDE 等国际主流期刊。
内容介绍：We propose and implement a structure-preserving stochastic particle method for the Landau equation. The method is based on a particle system for the Landau equation, where pairwise grazing collisions are modeled as diffusion processes. By exploiting the unique structure of the particle system and a spherical Brownian motion sampling, the method avoids additional temporal discretization of the particle system, ensuring that the discrete-time particle distributions exactly match their continuous-time counterparts. The method achieves $O(N)$ complexity per time step and preserves fundamental physical properties, including the conservation of mass, momentum and energy, as well as entropy dissipation. It demonstrates strong long-time accuracy and stability in numerical experiments. Furthermore, we also apply the method to the spatially non-homogeneous equations through a case study of the Vlasov--Poisson--Landau equation.