TY - JOUR
T1 - Motion by mean curvature of curves on surfaces using the Allen-Cahn equation
AU - Choi, Yongho
AU - Jeong, Darae
AU - Lee, Seunggyu
AU - Yoo, Minhyun
AU - Kim, Junseok
N1 - Funding Information:
The author (D. Jeong) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2014R1A6A3A01009812 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ). The authors are grateful to the anonymous referees, whose valuable suggestions and comments significantly improved the quality of this paper.
Publisher Copyright:
© 2015 Elsevier Ltd. All rights reserved.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - In this paper we develop a fast and accurate numerical method for motion by mean curvature of curves on a surface in three-dimensional space using the Allen-Cahn equation. We use a narrow band domain. We adopt a hybrid explicit numerical method which is based on an operator splitting method. First, we solve the heat equation by using an explicit standard Cartesian finite difference scheme. For the domain boundary cells, we use an interpolation using the closest point method. Then, we update the solution by using a closed-form solution. The proposing numerical algorithm is computationally efficient since we use a hybrid explicit numerical scheme and solve the governing equation only on the narrow domain. We perform a series of numerical experiments. The computational results are consistent with known analytic solutions.
AB - In this paper we develop a fast and accurate numerical method for motion by mean curvature of curves on a surface in three-dimensional space using the Allen-Cahn equation. We use a narrow band domain. We adopt a hybrid explicit numerical method which is based on an operator splitting method. First, we solve the heat equation by using an explicit standard Cartesian finite difference scheme. For the domain boundary cells, we use an interpolation using the closest point method. Then, we update the solution by using a closed-form solution. The proposing numerical algorithm is computationally efficient since we use a hybrid explicit numerical scheme and solve the governing equation only on the narrow domain. We perform a series of numerical experiments. The computational results are consistent with known analytic solutions.
KW - Allen-Cahn equation
KW - Closest point method
KW - Hybrid explicit scheme
KW - Motion by mean curvature
KW - Narrow band domain
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U2 - 10.1016/j.ijengsci.2015.10.002
DO - 10.1016/j.ijengsci.2015.10.002
M3 - Article
AN - SCOPUS:84945941627
VL - 97
SP - 126
EP - 132
JO - International Journal of Engineering Science
JF - International Journal of Engineering Science
SN - 0020-7225
ER -