勷勤数学•专家报告

题      目：Numerical Studies for Poisson-Nernst-Planck (PNP) System, Its Variant & Applications to Electrohydrodynamics

报  告  人：孙澎涛 教授  (邀请人：钟柳强)

                                   University of Nevada Las Vegas, UNLV

时      间：1月4日  16：00-17：00

地     点：数科院西楼二楼会议室

报告人简介:

       孙澎涛博士，现任美国内华达大学拉斯维加斯分校（University of Nevada Las Vegas, UNLV）数学系的终身正教授，博士生导师。1997年在中国科学院数学研究所获博士学位。在2007年入职美国内华达大学（UNLV）之前，曾先后在中国科学院、香港理工大学、美国宾夕法尼亚州立大学、加拿大西蒙弗雷泽大学担任博士后、副研究员、助理教授等职位。主要研究方向：偏微分方程数值解，有限元/有限体积方法的数值分析，自适应有限元方法，区域分解方法，相场方法，以及对流体动力学、固体力学、流─固耦合动力学、燃料电池动力学、血液动力学、电流体动力学等多物理场问题的建模、科学与工程计算的算法、分析、实现等研究。在著名的科学期刊上发表学术论文100余篇。2008年以来的研究课题连续被美国国家科学基金会（NSF），西蒙斯基金会（Simons Foundation）和内华达大学的教授研究奖励基金所资助。于2016年获得内华达大学理学院颁发的杰出研究奖。

摘      要：

       The Poisson-Nernst-Planck (PNP) system is one of commonly used models in theoretical and computational studies of biological ion channels, especially the fields of electro-kinetics and electro-hydrodynamics gained an increasing interest in recent years. In contrast to the limited amount of work on the numerical analysis, numerical computations with PNP equations have been widely conducted by computational physicists and biophysicists, and finite element method is most popularly adopted in recent years to solve the steady-state and time-dependent PNP system and its variants. However, finite element analyses of PNP equations are either incomplete or lack the accuracy. In this talk, I am going to address challenging problems in finite element analyses of PNP equations, then introduce our recent work on the a priori finite element error analysis for the time-dependent PNP equations, including both standard Galerkin method and mixed finite element method.
        We also developed and analyzed mixed finite element methods for PNP/Stokes coupling problem. Next, I will also address a new model called the fourth-order modified Poisson-Fermi equation resulted from the Bazant-Storey-Kornyshev (BSK) theory to account for electrostatic correlations in concentrated electrolytes, which induces an interesting phenomenon of charge inversion, present our development of corresponding FEMs, and numerical verifications & validations. Finally, I will introduce the application of PNP system to ion channels, and our future research plan on a realistic ionic fluid problem modeled by the transient PNP/Navier-Stokes coupling system.

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