An Adaptive Time-Stepping Algorithm for the Allen-Cahn Equationopen access
- Authors
- Lee, Chaeyoung; Park, Jintae; Kwak, Soobin; Kim, Sangkwon; Choi, Yongho; Ham, Seokjun; Kim, Junseok
- Issue Date
- 16-7월-2022
- Publisher
- HINDAWI LTD
- Citation
- JOURNAL OF FUNCTION SPACES, v.2022
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF FUNCTION SPACES
- Volume
- 2022
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/143357
- DOI
- 10.1155/2022/2731593
- ISSN
- 2314-8896
- Abstract
- In this paper, we present a simple and accurate adaptive time-stepping algorithm for the Allen-Cahn (AC) equation. The AC equation is a nonlinear partial differential equation, which was first proposed by Allen and Cahn for antiphase boundary motion and antiphase domain coarsening. The mathematical equation is a building block for modelling many interesting interfacial phenomena such as dendritic crystal growth, multiphase fluid flows, and motion by mean curvature. The proposed adaptive time-stepping algorithm is based on the Runge-Kutta-Fehlberg method, where the local truncation error is estimated by using fourth- and fifth-order numerical schemes. Computational experiments demonstrate that the proposed time-stepping technique is efficient in multiscale computations, i.e., both the fast and slow dynamics.
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Collections - College of Science > Department of Mathematics > 1. Journal Articles
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