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Random batch particle methods for the Poisson-Nernst-Planck, Poisson-Boltzmann and Fokker-Planck-Landau equations

组织者

李震 , 梁鑫 , 马志婷 , 哈米德·莫菲迪 , 王丽 , 熊繁升 , 杨朔 , 杨武岳

演讲者

汤一嘉

时间

2025年06月12日 15:00 至 16:00

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

Interacting particle systems can describe various phenomena in natural and social sciences. They can also be regarded as particle methods for mean field equations. However, direct simulation is expensive when N is large. The random batch method was proposed to overcome this difficulty. Based on a small but random batch idea, the computational cost can be reduced from O(N^2) to O(N) for binary interactions. In this talk, I will introduce efficient random batch particle methods for two classes of partial differential equations: i) the Poisson-Nernst-Planck equation and its equilibrium Poisson-Boltzmann equation in electrochemistry, ii)the Fokker-Planck-Landau equations in plasma physics. The particle methods for PNP and PB equations can also describe physical phenomena beyond the scope of the mean-field equations. For the FPL equations, the particle methods can preserve conservation and entropy dissipation properties.