Title: Regularization methods for the Poisson-Boltzmann model with sharp or diffuse interfaces

Abstract: 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.

This talk is based on joint works with Dr. Weihua Geng (Southern Methodist University), Dr. Yuanzhen Shao (University of Alabama), and Dr. Emil Alexov (Clemson University)