A practical adaptive grid method for the Allen–Cahn equation

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

Physica A: Statistical Mechanics and its Applications, 2021, vol. 573, issue C

Abstract: 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.

Keywords: Allen–Cahn equation; Adaptive grid; Finite difference scheme; Motion by mean curvature (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:573:y:2021:i:c:s0378437121002478

DOI: 10.1016/j.physa.2021.125975

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