应兰州大学数学与统计学院邀请，美国阿拉巴马大学数学系赵山教授将于2021年6月21日作线上学术报告。

报告题目：Regularization methods for the Poisson-Boltzmann model with sharp or diffuse interfaces

时    间：2021年6月21日上午9：00

地    点：腾讯会议（会议ID982884640未设密码）

摘    要：Both the sharp interface and diffuse interface Poisson-Boltzmann (PB) models have been presented in the literature for studying electrostatic interactions between a solute molecule and its surrounding solvent environment. In the mathematical analysis and numerical computation for these PB models, a significant 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 diffuse interface PB model, and investigated its convergence 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 the reaction-field potential and electrostatic free energy are rigorously proved. This convergence study enables us to unify the regularization for both sharp interface and diffuse interface PB models.

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赵山教授简介

1997年获兰州大学数学系学士学位，2003年获新加坡国立大学计算科学系博士学位，美国密歇根州立大学博士后。自2006年任教于美国阿拉巴马大学数学系，2015年提前晋升为数学系正教授。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，现已发表了70余篇SCI杂志论文，得到美国国家科学基金的连续资助。

甘肃省应用数学与复杂系统重点实验室

数学与统计学院

萃英学院

2021年6月17日