Abstract
We consider an unconditionally gradient stable scheme for solving the Allen-Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using eigenvalues of the Hessian matrix of the energy functional. We also show the pointwise boundedness of the numerical solution for the Allen-Cahn equation. We describe various numerical experiments we performed to study properties of the Allen-Cahn equation.
| Original language | English |
|---|---|
| Pages (from-to) | 1791-1803 |
| Number of pages | 13 |
| Journal | Physica A: Statistical Mechanics and its Applications |
| Volume | 388 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 2009 May 1 |
Bibliographical note
Funding Information:This research was supported by the MKE (Ministry of Knowledge Economy), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute for Information Technology Advancement) (IITA-2008- C1090-0801-0013). The first author (J.-W. Choi) was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005-041-C00073). The corresponding author (J.S. Kim) was also supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2008-C00044). The authors thank an anonymous referee for very useful comments on this paper.
Keywords
- Allen-Cahn equation
- Finite difference
- Nonlinear multigrid
- Unconditionally gradient stable
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics
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