Motion by Mean Curvature with Constraints Using a Modified Allen–Cahn Equation

Soobin Kwak, Hyun Geun Lee, Yibao Li, Junxiang Yang, Chaeyoung Lee, Hyundong Kim, Seungyoon Kang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this article, we present a simple and accurate computational scheme for motion by mean curvature with constraints using a modified Allen–Cahn (AC) equation. The modified AC equation contains a nonlinear source term which enforces the constraints such as volume and average mean curvature. We use a linear convex splitting-type method with Fourier spectral method to numerically solve the modified AC equation. We perform several characteristic computational tests to demonstrate the efficiency and accuracy of the proposed method. The computational results confirm the robust and high performance of the proposed algorithm.

Original languageEnglish
Article number16
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - 2022 Jul

Bibliographical note

Funding Information:
C. Lee was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2022R1C1C2003896). H. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Republic of Korea (NRF-2020R1A6A3A13077105). The corresponding author (J. Kim) was supported by Korea University Grant.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Finite difference method
  • Fourier spectral method
  • Motion by mean curvature
  • Phase-field model

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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