A practical adaptive grid method for the Allen–Cahn equation

Darae Jeong, Yibao Li, Yongho Choi, Chaeyoung Lee, Junxiang Yang, Junseok Kim

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We present a simple and practical adaptive finite difference method for the Allen–Cahn (AC) equation in the two-dimensional space. We use a temporally adaptive narrow band domain embedded in the uniform discrete rectangular domain. The narrow band domain is defined as a neighboring region of the interface. We employ a recently developed explicit hybrid numerical scheme for the AC equation. Therefore, the computational algorithm on the narrow band discrete domain is simple and fast. We demonstrate the high performance of the proposed adaptive method for the AC equation through various computational experiments.

Original languageEnglish
Article number125975
JournalPhysica A: Statistical Mechanics and its Applications
Publication statusPublished - 2021 Jul 1

Bibliographical note

Funding Information:
The first author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). This study was supported by 2018 Research Grant (PoINT) from Kangwon National University, Republic of Korea. Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416, No. 11631012). The corresponding author (J.S. 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-2019R1A2C1003053).

Publisher Copyright:
© 2021 Elsevier B.V.


  • Adaptive grid
  • Allen–Cahn equation
  • Finite difference scheme
  • Motion by mean curvature

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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