NUMERICAL ANALYSIS OF AN ODE AND A LEVEL SET METHODS FOR EVOLVING SPIRALS BY CRYSTALLINE EIKONAL-CURVATURE FLOW

In this paper, the evolution of a polygonal spiral curve by the crystalline curvature flow with a pinned center is considered from two viewpoints; a discrete model consisting of an ODE system describing facet lengths and another using level set method. We investigate the difference of these models numerically by calculating the area of an interposed region by their spiral curves. The area difference is calculated by the normalized L-1 norm of the difference of step-like functions which are branches of arg(x) whose discontinuities are on the spirals. We find that the differences in the numerical results are small, even though the model equations around the center and the farthest facet are slightly different.

Automated summary

This paper considers the evolution of a polygonal spiral curve under crystalline curvature flow with a pinned center from two viewpoints - a discrete model and one using the level set method. The differences between these models are investigated numerically by calculating the area of the interposed region by their spiral curves. It is found that the numerical results exhibit small differences, despite slight variations in the model equations around the center and the farthest facet.