A minimizing movements approach for crystalline eikonal-curvature flows of spirals

TL;DR

This paper introduces a novel algorithm for evolving spiral curves based on crystalline curvature using a minimizing movements approach and level set methods, with demonstrated numerical effectiveness.

Contribution

It presents a new numerical algorithm for crystalline eikonal-curvature flows of spirals, combining minimizing movements and level set techniques.

Findings

Numerical simulations show the algorithm effectively evolves spiral curves.

Comparisons demonstrate the method's accuracy and stability.

The approach advances computational methods for crystalline curvature flows.

Abstract

We propose an algorithm for evolving spiral curves on a planar domain by normal velocities depending on the so-called crystalline curvatures. The algorithm uses a minimizing movement approach and relies on a special level set method for embedding the spirals. We present numerical simulations and comparisons demonstrating the efficacy of the proposed numerical algorithm.