Numerical surgery for mean curvature flow of surfaces

10/25/2022

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by   Balazs Kovacs, et al.

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A numerical algorithm for mean curvature flow of surfaces with surgery is proposed. The method uses a convergent finite element based mean curvature flow algorithm based on a coupled partial differential equation system which directly provides an approximation for mean curvature and outward unit normal. The proposed numerical surgery process closely follows the analytical surgery of Huisken Sinestrari, and Brendle Huisken. The numerical surgery approach is described in detail, along with extensions to other geometric flows and methods. Numerical experiments report on the performance of the numerical surgery process.