参考文献/References:
[1] ALLEN S M,CAHN J W.A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening[J].Acta Metallurgica,1979,27(6):1085-1095.
[2] COHEN D S,MURRAY J D.A generalized diffusion model for growth and dispersal in a population[J].Journal of Mathematical Biology,1981,12(2):237-249.
[3] WHEELER A A,BOETTINGER W J,MCFADDEN G B.Phase-field model for isothermal phase transitions in binary alloys[J].Physical Review A:Atomic,Molecular,and Optical Physics,1992,45(10):7424-7439.
[4] HAZEWINKEL M,KAASHOEK J F,LEYNSE B.Pattern formation for a one dimensional evolution equation based on Thom's River basin model[M]//KILMISTER C W.Disequilibrium and self-organisation:mathematics and its applications.Dordrecht:Springer,1986:23-46.
[5] KIM JUNSEOK.Phase-field models for multi-component fluid flows[J].Communications in Computational Physics,2012,12(3):613-661.
[6] ZHAI Shuying,FENG Xinlong,HE Yinnian.Numerical simulation of the three dimensional Allen-Cahn equation by the high-order compact ADI method[J].Computer Physics Communications,2014,185(10):2449-2455.
[7] LI Congying,HUANG Yunqing,YI Nianyu.An unconditionally energy stable second order finite element method for solving the Allen-Cahn equation[J].Journal of Computational and Applied Mathematics,2019,353:38-48.
[8] FENG Xiaobing,LI Yukun.Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen-Cahn equation and the mean curvature flow[J].IMA Journal of Numerical Analysis,2015,35(4):1622-1651.
[9] EYRE D J.Unconditionally gradient stable time marching the Cahn-Hilliard equation[J].MRS Online Proceedings Library,1998,529:39-46.
[10] CHEN Longqing,SHEN Jie.Applications of semi-implicit Fourier-spectral method to phase field equations[J].Computer Physics Communications,1998,108(2/3):147-158.
[11] CHOI Jeongwhan,LEE Hyungeun,JEONG Darae,et al.An unconditionally gradient stable numerical method for solving the Allen-Cahn equation[J].Physica A:Statistical Mechanics and Its Applications,2009,388(9):1791-1803.
[12] YANG Xiaofeng,ZHAO Jia,WANG Qi.Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method[J].Journal of Computational Physics,2017,333:104-127.
[13] SHEN Jie,XU Jie,YANG Jiang.The scalar auxiliary variable(SAV)approach for gradient flows[J].Journal of Computational Physics,2018,353:407-416.
[14] LI Xiaoli,SHEN Jie,RUI Hongxing.Energy stability and convergence of SAV block-centered finite difference method for gradient flows[J].Mathematics of Computation,2019,88(319):2047-2068.
[15] SHEN Jie,XU Jie.Unconditionally bound preserving and energy dissipative schemes for a class of Keller-Segel equations[J].SIAM Journal of Numerical Analysis,2020,58(3):1674-1695.
[16] LI Xiaoli,SHEN Jie.Error analysis of the SAV-MAC scheme for the Navier-Stokes equations[J].SIAM Journal of Numerical Analysis,2020,58(5):2465-2491.
[17] HIGHAM N J.The numerical stability of barycentric Lagrange interpolation[J].IMA Journal of Numerical Analysis,2004,24(4):547-556.
[18] 李树忱,王兆清.高精度无网格重心插值配点法:算法、程序及工程应用[M].北京:科学出版社,2012.
[19] 虎晓燕,韩惠丽.重心插值配点法求解分数阶Fredholm积分方程[J].郑州大学学报(理学版),2017,49(1):17-23.
[20] 王兆清,徐子康.基于平面问题的位移压力混合配点法[J].计算物理,2018,35(1):77-86.
[21] 翁智峰,姚泽丰,赖淑琴.重心插值配点法求解Allen-Cahn方程[J].华侨大学学报(自然科学版),2019,40(1):133-140.
[22] YI Shichao,YAO Linquan.A steady barycentric Lagrange interpolation method for the 2D higher-order time-fractional telegraph equation with nonlocal boundary condition with error analysis[J].Numerical Methods for Partial Differential Equations,2019,35(5):1694-1716.
[23] GOLUB G H,VAN LOAN C F.Matrix computations[M].4th ed.Baltimore:Johns Hopkins University Press,2013.
[24] VAN LOAN C.Computational frameworks for the fast Fourier transform[M].Philadelphia:SIAM,1992.