Abstract: First, I will present some tailored alternating direction implicit (ADI) algorithms for solving nonlinear PDEs in biomolecular solvation analysis. Based on the variational formulation, we have previously proposed a pseudo-transient continuation model to couple a nonlinear Poisson–Boltzmann (NPB) equation for the electrostatic potential with a geometric flow equation defining the biomolecular surface. To speed up, we have reformulated the geometric flow equation so that an unconditionally stable ADI algorithm can be realized for molecular surface generation. Meanwhile, to overcome the stability issue associated with the strong nonlinearity, we have introduced an operator splitting ADI method for solving the NPB equation. Second, motivated by biomolecular solvation studies, we consider a parabolic interface problem. A novel matched ADI method is proposed to solve a 2D diffusion equation with material interfaces involving complex geometries. For the first time in the literature, the ADI finite difference method is able to deliver a second order of accuracy in space for arbitrarily shaped interfaces and spatial-temporal dependent interface conditions.

  

About the Speaker: Shan Zhao received the B.S. degree in mathematics from Lanzhou University, China, in 1997, and the Ph.D. degree in scientific computing from National University of Singapore, in 2003. From 2003 to 2006, he was a postdoctoral fellow with the Michigan State University. In 2006, he joined the Faculty of the Mathematics Department, University of Alabama, as an Assistant Professor. He was promoted to an Associate Professor of mathematics as of August 2011. Zhao’s current research interests include high-order methods for solving PDEs, computational electromagnetics and optics, high-order interface and boundary treatments, mathematical modeling of molecular surfaces in the implicit solvent theory, and fast biomolecular simulation.