Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Doctor Yifei Li,Department of Mathematics, National University of Singapore
Inviter:	Professor Weiying Zheng
Title:	A Structure-Preserving Parametric Finite Element Method of Anisotropic Geometric Flows
Language:	Chinese
Time & Venue:	2024.04.10 16:30-17:30 N733
Abstract:	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.