Numerical approximation of positive power curvature flow via deterministic games

2015/04/15 by Heiko Kröner, Kröner, Heiko
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical Analysis (math.NA) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1504.03997

openalex publication_date 2015/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

We approximate the level set solution for the motion of an embedded closed curve in the plane with normal speed max(0, κ)^\ga where κ is the curvature of the curve and (1)/(3)<\ga<1 by the value functions of a family of deterministic two person games. We show convergence of the value functions to the viscosity solution of the level set equation and propose a numerical scheme for the calculation of the value function.

Citations

• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Numerical approximation of level set power mean curvature flow

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