TY - JOUR
T1 - A hybrid FEM for solving the Allen-Cahn equation
AU - Shin, Jaemin
AU - Park, Seong Kwan
AU - Kim, Junseok
N1 - 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.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - 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.
AB - 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.
KW - Allen-Cahn equation
KW - Finite element method
KW - Operator splitting method
KW - Unconditionally stable scheme
UR - http://www.scopus.com/inward/record.url?scp=84905392025&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2014.07.040
DO - 10.1016/j.amc.2014.07.040
M3 - Article
AN - SCOPUS:84905392025
SN - 0096-3003
VL - 244
SP - 606
EP - 612
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -