Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations

IF 2.2 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

Journal of Computational Electronics Pub Date : 2023-09-26 DOI:10.1007/s10825-023-02092-y

Zhen Chao, Weihua Geng, Robert Krasny

引用次数: 0

Abstract

An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K\(^+\) ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.

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一维稳态Poisson-Nernst-Planck方程的积分方程方法

提出了一维稳态Poisson-Nernst-Planck方程的积分方程方法，用于模拟离子在膜通道中的传输。使用格林第三恒等式将微分方程重新定义为积分方程，从而产生电势梯度和离子浓度的定点问题。积分通过中点和梯形规则的组合进行离散，并通过Gummel迭代求解得到的代数方程。对电中性和非电中性系统的数值测试证明了该方法的二阶精度和分辨尖锐边界层的能力。该方法应用于具有固定电荷密度的K（^+\）离子通道的1D模型，以确保阳离子选择性。在这些测试中，所提出的积分方程方法产生的电势和浓度分布与已发表的结果非常一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Electronics ENGINEERING, ELECTRICAL & ELECTRONIC-PHYSICS, APPLIED

CiteScore

4.50

自引率

4.80%

发文量

142

审稿时长

>12 weeks

期刊介绍： he Journal of Computational Electronics brings together research on all aspects of modeling and simulation of modern electronics. This includes optical, electronic, mechanical, and quantum mechanical aspects, as well as research on the underlying mathematical algorithms and computational details. The related areas of energy conversion/storage and of molecular and biological systems, in which the thrust is on the charge transport, electronic, mechanical, and optical properties, are also covered. In particular, we encourage manuscripts dealing with device simulation; with optical and optoelectronic systems and photonics; with energy storage (e.g. batteries, fuel cells) and harvesting (e.g. photovoltaic), with simulation of circuits, VLSI layout, logic and architecture (based on, for example, CMOS devices, quantum-cellular automata, QBITs, or single-electron transistors); with electromagnetic simulations (such as microwave electronics and components); or with molecular and biological systems. However, in all these cases, the submitted manuscripts should explicitly address the electronic properties of the relevant systems, materials, or devices and/or present novel contributions to the physical models, computational strategies, or numerical algorithms.