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.
Original language | English |
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Article number | 125975 |
Journal | Physica A: Statistical Mechanics and its Applications |
Volume | 573 |
DOIs | |
Publication status | Published - 2021 Jul 1 |
Bibliographical note
Publisher Copyright:© 2021 Elsevier B.V.
Keywords
- Adaptive grid
- Allen–Cahn equation
- Finite difference scheme
- Motion by mean curvature
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics