Yifei Li, Doctor, Department of Mathematics, National University of Singapore

Weiying Zheng, Professor

A Structure-Preserving Parametric Finite Element Method of Anisotropic Geometric Flows

16:30-17:30 April 10 (Wednesday), N733

Designing a numerical scheme that can preserve the geometric structure for anisotropic geometric flows with an arbitrary anisotropic surface energy is a long-standing problem. In this talk, for anisotropic mean curvature flow and anisotroic surface diffusion, we propose and analyze a structure-preserving parametric finite element methods (SP-PFEM) for the evolution of a closed curve in 2D, which preserve two geometric structures – area conservation and energy dissipation – at the full-discretized level, The SP-PFEM innovates with a novel surface energy matrix and the Cahn-Hoffman ξ-vector, leading to a new geometric identity for dealing with the weighted mean curvature. This new geometric identity allows our SP-PFEM to be easily extended to various geometric flows with anisotropic effects. Extensive numerical results demonstrate its efficiency, stability, and success in other geometric flows.

报告人介绍：李逸飞 新加坡国立大学数学系博士后。本科毕业于北京大学，博士毕业于新加坡国立大学。主要研究几何流的保结构参数化有限元算法。