Abstract
We present an unconditionally stable hybrid finite element method for solving the Allen-Cahn equation, which describes the temporal evolution of a non-conserved phase-field during the antiphase domain coarsening in a binary mixture. Its various modified forms have been applied to image analysis, motion by mean curvature, crystal growth, topology optimization, and two-phase fluid flows. The hybrid method is based on the operator splitting method. The equation is split into a heat equation and a nonlinear equation. An implicit finite element method is applied to solve the diffusion equation and then the nonlinear equation is solved analytically. Various numerical experiments are presented to confirm the accuracy and efficiency of the method. Our simulation results are consistent with previous theoretical and numerical results.
| Original language | English |
|---|---|
| Pages (from-to) | 606-612 |
| Number of pages | 7 |
| Journal | Applied Mathematics and Computation |
| Volume | 244 |
| DOIs | |
| Publication status | Published - 2014 Oct 1 |
Bibliographical note
Funding Information:The author (J. Shin) is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). The corresponding author (J.S. Kim) was supported by a Korea University Grant. The authors also wish to thank the reviewers for the constructive and helpful comments on the revision of this article.
Keywords
- Allen-Cahn equation
- Finite element method
- Operator splitting method
- Unconditionally stable scheme
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics