报告摘要：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 formean 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, Yan Wang and Quan Zhao.

报告人简介：Professor Weizhu BAO is Provost's Chair Professor at Department of Mathematics, and Vice Dean for Graduate Studies and Academic Affairs of Faculty of Science, National University of Singapore.He got his PhD from Tsinghua University in 1995. He has made significant contributions in modeling and simulation of Bose-Einstein condensation, solid-state dewetting and geometric flows; and multiscale methods and analysis for highly oscillatory PDEs.He was awarded the Feng Kang Prize in Scientific Computing by the Chinese Computational Mathematics Society in 2013. He was an Invited Speaker at the International Congress of Mathematicians (ICM) in 2014. He was elected a Fellow of the American Mathematical Society (AMS Fellow), a Fellow of the Society of Industrial and Applied Mathematics (SIAM Fellow) and a Fellow of Singapore National Academy of Science (SNAS Fellow) in 2022. In 2024, he was elected as an Officer-at-large of the International Council of Industrial and Applied Mathematicians (ICIAM).