论文标题
Poisson-Nernst-Planck方程的动态质量传输方法
A dynamic mass transport method for Poisson-Nernst-Planck equations
论文作者
论文摘要
提出了一种动态质量传输方法，用于近似求解泊松 - 静脉planck（PNP）方程。基于JKO型变异配方的半混凝土方案自然会实现解决方案阳性和能量定律，例如连续的PNP系统。完全离散的方案被进一步提出为约束的最小化问题，可解决，并满足与时间步长或空间网格大小无关的所有三个溶液特性（质量保护，阳性和能量耗散）。进行数值实验以验证计算溶液的收敛性并验证所提出方案的结构保留特性。
A dynamic mass-transport method is proposed for approximately solving the Poisson-Nernst-Planck(PNP) equations. The semi-discrete scheme based on the JKO type variational formulation naturally enforces solution positivity and the energy law as for the continuous PNP system. The fully discrete scheme is further formulated as a constrained minimization problem, shown to be solvable, and satisfy all three solution properties (mass conservation, positivity and energy dissipation) independent of time step size or the spatial mesh size. Numerical experiments are conducted to validate convergence of the computed solutions and verify the structure preserving property of the proposed scheme.
