一种三维Poisson-Nernst-Planck方程的虚单元计算  

Virtual Element Computation for a Three-Dimensional Poisson-Nernst-Planck Equations

作　　者：丁聪 刘杨 阳莺[1] 沈瑞刚 DING Cong;LIU Yang;YANG Ying;SHEN Ruigang(Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guangxi Applied Mathematics Center(GUET),School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,Guangxi Zhuang Autonomous Region,China;School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,Hunan Province,China)

机构地区：[1]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 [2]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《吉林大学学报（理学版）》2024年第2期293-301,共9页Journal of Jilin University:Science Edition

基　　金：广西科技基地和人才专项基金(批准号:桂科AD23026048);国家自然科学基金(批准号:NSFC12161026,12101595)。

摘　　要：利用虚单元方法在多面体网格上求解一种三维稳态Poisson-Nernst-Planck(PNP)方程,并给出PNP方程的虚单元离散形式,推导电势方程及离子浓度方程的刚度矩阵与荷载向量的矩阵表达式.数值实验结果表明,在3种不同的多面体网格下实现了PNP方程的虚单元计算,数值解在L^(2)和H^(1)范数下均达到最优阶.The virtual element method was used to solve a three-dimensional steady-state Poisson-Nernst-Planck(PNP)equations on polyhedral meshes.The virtual element discrete forms of the PNP equations were given,and the matrix expressions of the stiffness matrix and the load vector of the electric potential equation and ion concentration equation were derived.The numerical experimental results show that the virtual element computation of PNP equations is realized in three different polyhedral meshes,and the numerical solutions reach the optimal order in both L^(2)and H^(2)norms.

关 键 词：Poisson-Nernst-Planck方程 虚单元方法 多面体网格 三维 

分 类 号：O241.82[理学—计算数学]