TY - JOUR
T1 - Fast and stable explicit operator splitting methods for phase-field models
AU - Cheng, Yuanzhen
AU - Kurganov, Alexander
AU - Qu, Zhuolin
AU - Tang, Tao
N1 - Funding Information:
The work of Y. Cheng, A. Kurganov and Z. Qu was supported in part by the NSF Grant # DMS-1115718. The research of T. Tang was supported in part by Hong Kong Research Grants Council CERG grants, the National Natural Science Foundation of China, and Hong Kong Baptist University FRG grants.
Publisher copyright:
Copyright © 2015 Elsevier Inc. All rights reserved.
PY - 2015/12/15
Y1 - 2015/12/15
N2 - Numerical simulations of phase-field models require long time computations and therefore it is necessary to develop efficient and highly accurate numerical methods. In this paper, we propose fast and stable explicit operator splitting methods for both one- and two-dimensional nonlinear diffusion equations for thin film epitaxy with slope selection and the Cahn-Hilliard equation. The equations are split into nonlinear and linear parts. The nonlinear part is solved using a method of lines together with an efficient large stability domain explicit ODE solver. The linear part is solved by a pseudo-spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. We demonstrate the performance of the proposed methods on a number of one- and two-dimensional numerical examples, where different stages of coarsening such as the initial preparation, alternating rapid structural transition and slow motion can be clearly observed.
AB - Numerical simulations of phase-field models require long time computations and therefore it is necessary to develop efficient and highly accurate numerical methods. In this paper, we propose fast and stable explicit operator splitting methods for both one- and two-dimensional nonlinear diffusion equations for thin film epitaxy with slope selection and the Cahn-Hilliard equation. The equations are split into nonlinear and linear parts. The nonlinear part is solved using a method of lines together with an efficient large stability domain explicit ODE solver. The linear part is solved by a pseudo-spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. We demonstrate the performance of the proposed methods on a number of one- and two-dimensional numerical examples, where different stages of coarsening such as the initial preparation, alternating rapid structural transition and slow motion can be clearly observed.
KW - Adaptive time-stepping
KW - Cahn-Hilliard equation
KW - Large stability domain explicit Runge-Kutta methods
KW - Molecular beam epitaxy equation
KW - Operator splitting methods
KW - Phase-field models
KW - Pseudo-spectral methods
KW - Semi-discrete finite-difference schemes
UR - http://www.scopus.com/inward/record.url?scp=84942902850&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2015.09.005
DO - 10.1016/j.jcp.2015.09.005
M3 - Journal article
AN - SCOPUS:84942902850
SN - 0021-9991
VL - 303
SP - 45
EP - 65
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -