Energy-stable parametric finite element methods (PFEM) for geometric PDEs and applications

• 主讲人：Prof. Weizhu Bao (National University of Singapore)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2023-03-10 16:00 - 2023-03-10 17:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/75E4F78ABA835368BBC9736011785A8E
Valid Until: 2027-04-30 23:59

 

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 semi-implicit parametric finite element method (PFEM) is presented in detail. 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.

 

Bio: Weizhu BAO is a Professor at the Department of Mathematics, National University of Singapore (NUS). He got his PhD from Tsinghua University in 1995 and afterwards he had postdoc and faculty positions at Tsinghua University, Imperial College, Georgia Institute of Technology and the University of Wisconsin at Madison. His research interests include numerical methods for partial differential equations, scientific computing/numerical analysis, analysis and computation for problems from physics, chemistry, biology and engineering sciences. He has made significant contributions in modeling and simulation of Bose-Einstein condensation, solid-state dewetting and geometric PDEs; and in multiscale methods and analysis for highly oscillatory PDEs. He had been on the Editorial Board of SIAM Journal on Scientific Computing during 2009--2014 and is currently on the Editorial Board of SIAM Journal of Numerical Analysis. He was awarded the Feng Kang Prize in Scientific Computing by the Chinese Computational Mathematics Society in 2013. Weizhu Bao was an invited speaker at the ICM 2014 in Seoul. He is a Fellow of the American Mathematical Society, the Society of Industrial and Applied Mathematics and the Singapore National Academy of Science.