报告题目：Some related work on Poisson-Nernst-Planck system
摘要：In this talk, I will show two parts of our recent work on Poisson-Nernst-Planck system.
The first part is the asymptotic solution of 1D steady state Poisson-Nernst-Planck system with multi-ions. This asymptotic solution is based on the classical matched asymptotic technics.
This part is based on the work
X. Wang, D. He, J. Wylie, H. Huang, Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems, Physical Review E, 89, 022722, 2014.
The second part is the energy preserving numerical methods for the unsteady Poisson-Nernst-Planck system by using both the finite difference method and finite element method.
This part is based on the following work
1. D. He and K. Pan, An energy preserving finite difference scheme for the Poisson-Nernst-Planck system. Applied Mathematics and Computation, 287-288(5) (2016) 214-223.
2. H. Gao and D. He, Linearized Conservative Finite Element Methods for the Nernst-Planck-Poisson Equations. Journal of Scientific Computing, 72(3) (2017) 1269–1289.
Dr. He is an associate Professor at School of Aerospace Engineering and Applied Mechanics, Tongji University. He received PhD in Applied Mathematics at York University (Canada) in 2012 under supervision of Prof. Huaxiong Huang. Before joining Tongji University, he worked as a postdoctoral fellow at Department of Mathematics in City University of Hong Kong, his postdoc advisor is Prof. Jonathan, Wylie.
Dr. He's research interests include Mathematical Modeling, Applied Asymptotic Analysis, Computational Fluid Mechanics and Numerical Methods for PDEs. He has published 20 refereed journal papers, which include publications in Journal of Fluid Mechanics, Journal of Computational Physics, Physical Review E, Journal of Scientific Computing, Communications in Computational Physics, Nonlinear Dynamics, Computers & Mathematics with Application, etc.