BIMSA > BIMSA Computational Math Seminar Random batch particle methods for the Poisson-Nernst-Planck, Poisson-Boltzmann and Fokker-Planck-Landau equations
Random batch particle methods for the Poisson-Nernst-Planck, Poisson-Boltzmann and Fokker-Planck-Landau equations
Organizers
Zhen Li , Xin Liang , Zhiting Ma , Hamid Mofidi , Li Wang , Fansheng Xiong , Shuo Yang , Wuyue Yang
Speaker
Yijia Tang
Time
Thursday, June 12, 2025 3:00 PM - 4:00 PM
Venue
Online
Online
Zoom 787 662 9899 (BIMSA)
Abstract
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.