应用数学青年讨论班（午餐会）—— A Structure-Preserving Parametric Finite Element Method of Anisotropic Geometric Flows

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.

Brief bio:

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。

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