Regularization methods for the Poisson-Boltzmann model with piecewise or heterogeneous dielectric functions
科研大讨论系列报告
报告题目(Title)：Regularization methods for the Poisson-Boltzmann model with piecewise or heterogeneous dielectric functions
报告人(Speaker)：Shan Zhao (Department of Mathematics, University of Alabama)
地点(Place)：后主楼1220
时间(Time)：2023年6月30日(周五), 16:00-17:00
邀请人(Inviter)：曹外香
报告摘要
Calculations of electrostatic potential and solvation energy of macromolecules are essential for understanding the mechanism of many biological processes. The classical sharp interface Poisson-Boltzmann (PB) model treats the solute molecule and its surrounding solvent as piecewise constant dielectric media, while the recently developed Gaussian PB models capture the atomic details by using atom-specific heterogeneous dielectric values. In all PB models, a significant numerical challenge is due to singular charge sources in terms of Dirac delta distributions. To overcome this difficulty, various regularization methods have been developed to analytically capture the solution singularities in the sharp interface PB model. Recently, we have compared four such regularization schemes in terms of accuracy and efficiency. More recently, we have developed the first regularization method for the PB models with diffuse interface or super-Gaussian dielectric functions, in which a dual decomposition is proposed for potential and dielectric functions. Most recently, we have investigated the convergence of the PB model when the diffused Gaussian-convolution surface (GCS) approaches to the sharp solvent accessible surface (SAS). Due to the limitation in numerical algorithm and mesh resolution, such a convergence is impossible to be realized numerically. Through analysing the weak solution for the regularized PB equations, the convergences for both potential and energy are rigorously proved. This convergence study enables us to unify the regularization for all PB models.
主讲人简介
赵山教授于 1997年在兰州大学数学系毕业取得学士学位, 2003年在新加坡国立大学计算科学系取得博士学位。2003年至2006年他在美国密歇根州立大学进行博士后研究。2006年开始在美国阿拉巴马大学(University of Alabama)数学系任助理教授(tenure-track)，于2012年取得终身教职(tenured) 和副教授，于2015年提前晋升为数学系正教授。赵山教授已指导了10名博士研究生和3名博士后。
赵山教授在分子生物学，计算电磁学，工程计算等交叉学科开展了包括数学建模，数值分析，和算法创新在内的一系列基础研究工作，已做出很多受到国际同行认可的创新性学术成就。他现已发表了70余篇SCI 杂志论文，其中一篇于2020年荣获世界华人数学家联盟(ICCM)最佳论文若琳奖。根据Google Scholar索引，他的论文被同行引用了超过2500次 。赵山教授的研究得到了美国国家科学基金长年的连续资助，一共主持过六项科研项目。赵山教授担任多家国际期刊的责任编委，编委，或客席编委，他也曾为50多家国际期刊担任论文评审人。
