The Poisson-Nernst-Planck (PNP) type of equations are one of the most extensively studied models for the transport of charged particles in many physical and biological problems. The solution to the PNP equations has many properties of physical importance, e.g., positivity, mass conservation, energy dissipation. It is desirable to design numerical methods that are able to preserve such properties at discrete level. In this talk, we will present two types of numerical schemes that can maintain physical properties. One is based on the so-called Slotboom variables; the other is based on the gradient flow structure of the PNP equations. Theoretical numerical analysis is presented to show that both numerical schemes can preserve physical properties. Some numerical results are shown to demonstrate their performances. This is a joint work with Jie Ding, Chun Liu, Cheng Wang, Zhongming Wang, Xingye Yue, and many others..
周圣高，上海交通大学长聘副教授。2012年在浙江大学获得理学博士学位，2012年-2015年在UCSD从事博士后研究。长期从事生物物理可计算建模和数值方法、分子动力学模拟和随机算法、计算化学和药物设计等方面的研究。以第一作者或通讯作者在PNAS，Math. Comput., SIAM J. Appl. Math., SIAM J. Sci. Comput., J. Comput. Phys.等杂志发表论文。