An explicit hybrid method for the nonlocal Allen-Cahn equation

Chaeyoung Lee, Sungha Yoon, Jintae Park, Junseok Kim

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We extend the explicit hybrid numerical method for solving the Allen-Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.

Original languageEnglish
Article number1218
Issue number8
Publication statusPublished - 2020 Aug

Bibliographical note

Funding Information:
Funding: The first author (C. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2019R1A6A3A13094308). The corresponding author (J.S. Kim) expresses thanks for the support from the BK21 PLUS program.

Publisher Copyright:
© 2020 by the authors.


  • Explicit hybrid method
  • Nonlocal allen-cahn equation
  • Operator splitting
  • Space-time dependent lagrange multiplier

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)


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