Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 60, Issue 6, Pages 1591-1606Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2010.06.041
Keywords
Allen-Cahn equation; Finite difference; Unconditionally stable; Operator splitting; Motion by mean curvature
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Funding
- Ministry of Education, Science and Technology [2009-0074248]
- National Research Foundation of Korea [2009-0074248] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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We present an unconditionally stable second-order hybrid numerical method for solving the Allen-Cahn equation representing a model for antiphase domain coarsening in a binary mixture. The proposed method is based on operator splitting techniques. The Allen-Cahn equation was divided into a linear and a nonlinear equation. First, the linear equation was discretized using a Crank-Nicolson scheme and the resulting discrete system of equations was solved by a fast solver such as a multigrid method. The nonlinear equation was then solved analytically due to the availability of a closed-form solution. Various numerical experiments are presented to confirm the accuracy, efficiency, and stability of the proposed method. In particular, we show that the scheme is unconditionally stable and second-order accurate in both time and space. (C) 2010 Elsevier Ltd. All rights reserved.
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