主講人：杜愷 復(fù)旦大學(xué)副教授

時(shí)間：2025年9月4日10：30

地點(diǎn)：三號(hào)樓332室 

舉辦單位：數(shù)理學(xué)院 

主講人介紹：杜愷，復(fù)旦大學(xué)上海數(shù)學(xué)中心長(zhǎng)聘副教授、博士生導(dǎo)師。2011年獲復(fù)旦大學(xué)博士學(xué)位，曾任職于蘇黎世聯(lián)邦理工學(xué)院 (ETH)、澳大利亞 Wollongong 大學(xué)。主要研究方向包括隨機(jī)分析、偏微分方程、最優(yōu)控制、強(qiáng)化學(xué)習(xí)等，成果發(fā)表于 PTRF、TAMS、SICON、JDE 等國(guó)際主流期刊。 

內(nèi)容介紹：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.