报告题目：Finite ElementMethods for System of Poisson-Nernst-Planck (PNP) Equations, Its Variant &Applications to Ion Channels
报告时间：2023年4月6日15:00-16:00
报告地点：红瓦楼726
报告人简介：Dr. Pengtao Sun (孙澎涛) is a Full Professorof Department of Mathematical Sciences in University of Nevada, Las Vegas (UNLV).Dr. Sun obtained his PhD degree from Institute of Mathematics, Chinese Academyof Sciences in 1997. Before joining University of Nevada, Las Vegas in 2007, heworked as Research Scientist, Postdoctoral Fellow, Research Associate andAssistant Professor in Chinese Academy of Sciences, The Hong Kong PolytechnicUniversity, Pennsylvania State University and Simon Fraser University. Dr Sun’sprimary research fields are Numerical PDEs and Scientific & EngineeringComputing with applications to miscellaneous multiphysics problems in thefields of solid mechanics, fluid dynamics, fuel cell dynamics, fluid-structure interactions,hemodynamics, electrohydrodynamics, and etc. Dr. Sun’s research has beencontinuously supported by National Science Foundation, Simons Foundation, and UNLV’sFaculty Opportunity Awards since 2008. Dr. Sun was the recipient of Distinguished ResearcherAward at College of Sciences, UNLV in 2016.
报告摘要：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 equations. However, the finite element analyses of PNP equations are either incomplete or lack the accuracy. In this talk, I am going to address the challenging problems in the finite element analysis 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 the mixed finite element method for PNP/Stokes coupling problem. Next, I will also talk about 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, and the development of corresponding FEMs. 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/Stokes coupling system.
报告时间：2023年4月6日15:00-16:00
报告地点：红瓦楼726
报告人简介：Dr. Pengtao Sun (孙澎涛) is a Full Professorof Department of Mathematical Sciences in University of Nevada, Las Vegas (UNLV).Dr. Sun obtained his PhD degree from Institute of Mathematics, Chinese Academyof Sciences in 1997. Before joining University of Nevada, Las Vegas in 2007, heworked as Research Scientist, Postdoctoral Fellow, Research Associate andAssistant Professor in Chinese Academy of Sciences, The Hong Kong PolytechnicUniversity, Pennsylvania State University and Simon Fraser University. Dr Sun’sprimary research fields are Numerical PDEs and Scientific & EngineeringComputing with applications to miscellaneous multiphysics problems in thefields of solid mechanics, fluid dynamics, fuel cell dynamics, fluid-structure interactions,hemodynamics, electrohydrodynamics, and etc. Dr. Sun’s research has beencontinuously supported by National Science Foundation, Simons Foundation, and UNLV’sFaculty Opportunity Awards since 2008. Dr. Sun was the recipient of Distinguished ResearcherAward at College of Sciences, UNLV in 2016.
报告摘要：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 equations. However, the finite element analyses of PNP equations are either incomplete or lack the accuracy. In this talk, I am going to address the challenging problems in the finite element analysis 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 the mixed finite element method for PNP/Stokes coupling problem. Next, I will also talk about 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, and the development of corresponding FEMs. 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/Stokes coupling system.