English

Numerical surgery for mean curvature flow of surfaces

Numerical Analysis 2023-09-22 v3 Numerical Analysis

Abstract

A numerical algorithm for mean curvature flow of closed mean convex surfaces with surgery is proposed. The method uses a 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.

Keywords

Cite

@article{arxiv.2210.14046,
  title  = {Numerical surgery for mean curvature flow of surfaces},
  author = {Balázs Kovács},
  journal= {arXiv preprint arXiv:2210.14046},
  year   = {2023}
}