Motion by mean curvature of curves on surfaces using the Allen-Cahn equation

Yongho Choi, Darae Jeong, Seunggyu Lee, Minhyun Yoo, Junseok Kim

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In this paper we develop a fast and accurate numerical method for motion by mean curvature of curves on a surface in three-dimensional space using the Allen-Cahn equation. We use a narrow band domain. We adopt a hybrid explicit numerical method which is based on an operator splitting method. First, we solve the heat equation by using an explicit standard Cartesian finite difference scheme. For the domain boundary cells, we use an interpolation using the closest point method. Then, we update the solution by using a closed-form solution. The proposing numerical algorithm is computationally efficient since we use a hybrid explicit numerical scheme and solve the governing equation only on the narrow domain. We perform a series of numerical experiments. The computational results are consistent with known analytic solutions.

Original languageEnglish
Pages (from-to)126-132
Number of pages7
JournalInternational Journal of Engineering Science
Volume97
DOIs
Publication statusPublished - 2015 Dec 1

Keywords

  • Allen-Cahn equation
  • Closest point method
  • Hybrid explicit scheme
  • Motion by mean curvature
  • Narrow band domain

ASJC Scopus subject areas

  • Engineering(all)

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