Shape transformation using the modified Allen–Cahn equation

Hyundong Kim, Sungha Yoon, Jian Wang, Chaeyoung Lee, Sangkwon Kim, Jintae Park, Junseok Kim

Research output: Contribution to journalArticle

Abstract

In this paper, we propose a phase-field model for the shape transformation and its simple numerical method. The proposed phase-field model is based on the Allen–Cahn equation, which is a second-order nonlinear parabolic partial differential equation and originally arises from modeling phase separation in alloys. The numerical scheme is a hybrid method using the operator splitting method. To validate the proposed phase-field model for the shape transformation, we perform two- and three-dimensional shape metamorphosis. The proposed phase-field model is also compared with the linear interpolation. The computational results demonstrate that the proposed mathematical model satisfactorily and naturally simulate the shape transformation.

Original languageEnglish
Article number106487
JournalApplied Mathematics Letters
Volume107
DOIs
Publication statusPublished - 2020 Sep

Keywords

  • Allen–Cahn equation
  • Metamorphosis
  • Phase-field
  • Shape transformation

ASJC Scopus subject areas

  • Applied Mathematics

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