Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations  

作　　者：Lei Li Jian-Guo Liu Yijia Tang 

机构地区：[1]School of Mathematical Sciences,Institute of Natural Sciences,MOE-LSC,Shanghai Jiao Tong University,Shanghai,200240,P.R.China [2]Department of Mathematics and Department of Physics,Duke University,Durham,NC 27708,USA [3]School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai,200240,P.R.China

出　　处：《Communications in Computational Physics》2022年第6期41-82,共42页计算物理通讯（英文）

基　　金：This work is partially supported by the National Key R&D Program of China,Project Number 2021YFA1002800;The work of L.Li was partially sponsored by the Strategic Priority Research Program of Chinese Academy of Sciences,Grant No.XDA25010403,and NSFC 11901389,12031013;The work of J.-G.Liu was supported by NSF DMS-2106988.

摘　　要：We consider in this paper random batch interacting particle methods forsolving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann(PB) equation as the equilibrium, in the external unbounded domain. To justify thesimulation in a truncated domain, an error estimate of the truncation is proved inthe symmetric cases for the PB equation. Then, the random batch interacting particle methods are introduced which are O(N) per time step. The particle methods cannot only be considered as a numerical method for solving the PNP and PB equations,but also can be used as a direct simulation approach for the dynamics of the chargedparticles in solution. The particle methods are preferable due to their simplicity andadaptivity to complicated geometry, and may be interesting in describing the dynamics of the physical process. Moreover, it is feasible to incorporate more physical effectsand interactions in the particle methods and to describe phenomena beyond the scopeof the mean-field equations.

关 键 词：Interacting particle systems Coulomb interaction reflecting stochastic differential equation charge reversal phenomenon singular-regular decomposition 

分 类 号：O17[理学—数学]