Speaker: Chunmei Wang, University of Florida

Title: "Efficient Numerical Methods for Weak Solutions of Partial Differential Equations"

Abstract: Approximating weak solutions of partial differential equations (PDEs) is known to be important and extremely challenging in scientific computing and data science. In this talk, the speaker will discuss two kinds of numerical methods for weak solutions: (1) Primal-Dual Weak Galerkin (PDWG) finite element methods for low-dimensional PDEs; and (2) Deep Learning methods (Friedrichs Learning) for high-dimensional PDEs. The essential idea of PDWG is to interpret the numerical solutions as a constrained minimization of some functionals with constraints that mimic the weak formulation of the PDEs by using weak derivatives. The resulting Euler-Lagrange formulation results in a symmetric scheme involving both the primal variable and the dual variable (Lagrangian multiplier). Friedrichs Learning is a novel deep learning methodology that could learn the weak solutions of PDEs via a mini-max optimization characterization of the original problem. The speaker will explain what Friedrichs Learning is and how it can be used for solving PDEs with discontinuous solutions without any prior knowledge of the solution discontinuity.

Bio: Chunmei Wang got her PhD in computational mathematics from Nanjing Normal University in 2014. She was a postdoc at Georgia Tech from 2014 to 2016. After that, she was an assistant professor at  Texas State University for two years and then at Texas Tech University for three years. She is currently an assistant professor at University of Florida starting from 2021. Her research interests include Numerical Partial Differential Equations, Finite Element Methods and Superconvergence, Weak Galerkin Finite Element Methods and Deep Learning for PDEs.

Please email [email protected] ahead of time for the Zoom link.