求解PNP方程的虚单元两水平算法

吉林大学学报(理学版) ›› 2025, Vol. 63 ›› Issue (4): 1051-1058.

求解PNP方程的虚单元两水平算法

毛万涛, 阳莺

桂林电子科技大学数学与计算科学学院, 广西应用数学中心(GUET), 广西高校数据分析与计算重点实验室, 广西桂林 541004

收稿日期:2024-10-08 出版日期:2025-07-26 发布日期:2025-07-26
通讯作者: 阳莺 E-mail:yangying@lsec.cc.ac.cn

Virtual Element Two-Level Algorithm for Solving PNP Equations

MAO Wantao, YANG Ying

Guangxi Applied Mathematics Center (GUET), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics & Computing Science, Guilin University of Electronic Technology, Guilin 541004, Guangxi Zhuang Autonomous Region, China

Received:2024-10-08 Online:2025-07-26 Published:2025-07-26

摘要/Abstract

摘要： 针对稳态和含时两种PNP(Poisson-Nernst-Planck)方程, 提出一种基于虚单元离散的两水平算法. 该算法先利用线性虚单元解对PNP方程进行解耦和线性化, 然后在二次虚单元空间上求解. 与PNP方程求解常用的Gummel算法相比, 该算法能加快求解速度. 包含稳态和含时两种PNP方程的数值实验结果表明, 与线性虚单元的Gummel算法相比, 两水平算法精度更高, 且在相当精度下, 耗费CPU时间更少, 效率更高.

关键词: Poisson-Nernst-Planck方程, 虚单元方法, 两水平算法, Gummel算法

Abstract: We proposed a two-level algorithm based on the virtual element discretization for both steady-state and time-dependent PNP (Poisson-Nernst-Planck) equations. This algorithm first decoupled and linearized the PNP equations using the linear virtual element solution, and then solved them in the quadratic virtual element space. Compared with the commonly used Gummel algorithm for solving the PNP equations, this algorithm could accelerate the solving speed. Numerical experimental results, including both
steady-state and time-dependent PNP equations, show that compared with the Gummel algorithm with the linear virtual element, the two-level algorithm has higher accuracy, and consumes less CPU time and is more efficient at comparable accuracy.

Key words: Poisson-Nernst-Planck equations, virtual element method, two-level algorithm, Gummel algorithm

中图分类号:

O241.82

毛万涛, 阳莺. 求解PNP方程的虚单元两水平算法[J]. 吉林大学学报(理学版), 2025, 63(4): 1051-1058.

MAO Wantao, YANG Ying. Virtual Element Two-Level Algorithm for Solving PNP Equations[J]. Journal of Jilin University Science Edition, 2025, 63(4): 1051-1058.

[1]	韦鹏, 沈瑞刚. 一类含时Poisson-Nernst-Planck方程的时间自适应计算[J]. 吉林大学学报(理学版), 2024, 62(6): 1352-1358.
[2]	丁聪, 刘杨, 阳莺, 沈瑞刚. 一种三维Poisson-Nernst-Planck方程的虚单元计算[J]. 吉林大学学报(理学版), 2024, 62(2): 293-0301.
[3]	倪宇晖, 阳莺. 一类Poisson-Nernst-Planck方程的边平均有限元计算[J]. 吉林大学学报(理学版), 2022, 60(1): 73-0078.