论文标题
一些用于泊松 - 尼斯特省和泊松玻璃到泊松的随机批处理粒子方法
Some random batch particle methods for the Poisson-Nernst-Planck and Poisson-Boltzmann equations
论文作者
论文摘要
我们在本文中考虑了用于求解Poisson-Nernst-Planck（PNP）方程的随机批次相互作用的粒子方法，从而在外部无界域中将Poisson-Boltzmann（Pb）方程作为平衡。为了证明截断域中的仿真合理，在PB方程的对称情况下证明了截断的误差估计值。然后，引入了随机批处理粒子方法，该方法是每个时间步的$ O（n）$。粒子方法不仅可以被视为求解PNP和PB方程的数值方法，而且还可以用作解决方案中带电粒子动力学的直接模拟方法。由于粒子方法的简单性和对复杂几何形状的适应性，因此更可取，并且在描述物理过程的动力学时可能很有趣。此外，可以在粒子方法中纳入更多的物理效应和相互作用并描述超出平均场方程范围的现象是可行的。
We consider in this paper random batch interacting particle methods for solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann (PB) equation as the equilibrium, in the external unbounded domain. To justify the simulation in a truncated domain, an error estimate of the truncation is proved in the 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 can not 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 charged particles in solution. The particle methods are preferable due to their simplicity and adaptivity to complicated geometry, and may be interesting in describing the dynamics of the physical process. Moreover, it is feasible to incorporate more physical effects and interactions in the particle methods and to describe phenomena beyond the scope of the mean-field equations.
