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A practical adaptive grid method for the Allen-Cahn equation
- Issue Date
- 1-7월-2021
- Publisher
- ELSEVIER
- Keywords
- Allen-Cahn equation; Adaptive grid; Finite difference scheme; Motion by mean curvature
- Citation
- PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v.573
- Indexed
- SCIE
SCOPUS
- Journal Title
- PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
- Volume
- 573
- ISSN
- 0378-4371
- 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. (C) 2021 Elsevier B.V. All rights reserved.
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