The Department of Applied Mathematics is presenting a seminar on Tuesday, April 15, 2025, at 12:45–1:45 p.m. in the John T. Rettaliata Engineering Center, room 102. Speaker Weizhu Bau, a professor from National University of Singapore, will give a talk titled “A structure-preserving parametric finite element method for geometric PDEs and applications.”

Abstract

In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow, surface diffusion flow, Willmore flow, etc., which arise from materials science, interface dynamics in multi-phase flows, biology membrane, computer graphics, geometry, etc. Different mathematical formulations and numerical methods for mean curvature flow are then discussed. In particular, an energy-stable linearly implicit parametric finite element method (PFEM) is presented in details. Then the PFEM is extended to surface diffusion flow and anisotropic surface diffusion flow, and a structure-preserving implicit PFEM is proposed. Finally, sharp interface models and their PFEM approximations are presented for solid-state dewetting. This talk is based on joint works with Harald Garcke, Wei Jiang, Yifei Li, Robert Nuernberg, Tiezheng Qian, David Srolovitz, Yan Wang and Quan Zhao.