Numerical analysis of an ode and a level set methods 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 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 L1 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.

Original languageEnglish
Pages (from-to)893-907
Number of pages15
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume14
Issue number3
DOIs
Publication statusPublished - 2021 Mar

Keywords

  • Crystalline eikonal-curvature flow
  • Evolution of a polygonal spiral
  • Finite difference scheme
  • Level set method
  • ODE system for crystalline motion

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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