Numerical analysis comparing ode approach and level set method for evolving spirals by crystalline eikonal-curvature flow

Tetsuya Ishiwata, Takeshi Ohtsuka

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, the evolution of a polygonal spiral curve by the crystalline curvature ow with a pinned center is considered with two view points, discrete model consist of an ODE system of facet lengths and a level set method. We investigate the difference of these models numerically by calculating the area of the region enclosed by these spiral curves. The area difference is calculated by the normalized L1 norm of the difference of step-like functions which are branches of arg x whose discontinuities are only on the spirals. Wefind the differences of the numerical results considered in this paper are very small even though the evolution laws of these models around the center and the farthest facet are slightly different.

34A34, 53C44 (Primary) 53A04 (Secondary)

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Jan 26

Keywords

  • Crystalline eikonal-curvature flow
  • Evolution of a polygonal spiral
  • Level set method

ASJC Scopus subject areas

  • General

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