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

4 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


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


Dive into the research topics of 'A practical adaptive grid method for the Allen–Cahn equation'. Together they form a unique fingerprint.

Cite this