Hailiang Liu, Professor, Lowa State University, USA

Xianmin Xu, Professor

A dynamic mass-transport method for Poisson-Nernst-Planck systems

15:00-16:00 July 5 (Wednesday), N202

In this talk, I will present some recent work on developing structure preserving (i.e., positivity preserving, mass conservative, and energy dissipating) methods for numerically simulating Poisson-Nernst-Planck (PNP) systems. Motivated by Benamou-Brenier's dynamic formulation of the quadratic Wasserstein metric, we introduce a Wasserstein-type distance suitable for our problem setting, we then construct a variational scheme which falls into the Jordan--Kinderlehrer--Otto framework. The variational scheme is a first order (in time) approximation of the original PNP system. To reduce computational cost, we further approximate the constraints and the objective function in the underlying Wasserstein-type distance, such approximations won't destroy the first order accuracy. With a standard spatial discretization, we obtain a finite dimensional strictly convex minimization problem with linear constraints. The admissible set in the variational problem is a subset of the probability space and the Wasserstein-type distance is nonnegative, therefore our scheme is a positivity preserving, mass conservative, and energy dissipating scheme.

报告人简介：Hailiang Liu is a Professor of Mathematics and Computer Science at the Iowa State University (ISU). He earned his Bachelor degree from Henan Normal University, Master degree from Tsinghua University, and Ph.D. degree from the Chinese Academy of Sciences, all in Mathematics. His research interests include analysis of partial differential equations, the development of high order numerical algorithms for solving these PDE problems, with diverse applications. He is the recipient of many awards and honors, including the Alexander von Humboldt-Research Fellowship, and the inaugural Holl Chair in Applied Mathematics. He is the author of over 160 peer reviewed papers. His recent work has focused on the study of data-driven deep learning problems.