Stochastic and Multiscale Modeling and Computational Seminar by Weizhu Bao: A Structure-Preserving Parametric Finite Element Method for Geometric PDEs and Applications
Speaker: Provost's Chair Professor of Mathematics, National University of Singapore.
Title: 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.
Stochastic and Multiscale Modeling and Computational Seminar