[1]刘佳奇,蔡耀雄,翟术英.空间分数阶Allen-Cahn方程的高效算子分裂格式[J].华侨大学学报(自然科学版),2022,43(6):833-839.[doi:10.11830/ISSN.1000-5013.202108033]
　LIU Jiaqi,CAI Yaoxiong,ZHAI Shuying.High Efficient Operator Splitting Scheme of Space-Fractional Allen-Cahn Equation[J].Journal of Huaqiao University(Natural Science),2022,43(6):833-839.[doi:10.11830/ISSN.1000-5013.202108033]
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空间分数阶Allen-Cahn方程的高效算子分裂格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第43卷
期数:
2022年第6期
页码:
833-839
栏目:
出版日期:
2022-11-11

文章信息/Info

Title:
High Efficient Operator Splitting Scheme of Space-Fractional Allen-Cahn Equation
文章编号:
1000-5013(2022)06-0833-07
作者:
刘佳奇;  蔡耀雄;  翟术英
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
LIU Jiaqi;  CAI Yaoxiong;  ZHAI Shuying
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
空间分数阶Allen-Cahn方程;  生成函数;  分数阶Laplace算子;  算子分裂法
Keywords:
spatial-fractional Allen-Cahn equation;  generating function;  fractional Laplace operator;  operator splitting method
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.202108033
文献标志码:
A
摘要:
基于算子分裂思想,将空间分数阶Allen-Cahn方程分解为非线性方程和分数阶热传导方程,其中,非线性方程有解析解,分数阶热传导方程可利用生成函数的方法结合Crank-Nicolson格式建立差分格式.通过数值算例验证格式的有效性.结果表明:空间分数阶Allen-Cahn方程的高效算子分裂格式具有稳定性、收敛性及有效性.
Abstract:
Based on the operator splitting thaught, the space-fractional Allen-Cahn equation can be decomposed into a nonlinear equation and a fractional heat conduction equation. Among them, a nonlinear equation has analytical solution. For the fractional heat conduction equation, a difference scheme is established by using the generating function method and the Crank-Nicolson scheme. Numerical experiments are given to verify the effectiveness of the form. The result shows that the efficient operator splitting scheme of the spatial-fractional Allen-Cahn equation is of the stability, convergence and effectiveness.

参考文献/References:

[1] 汪精英,邓杨芳,翟术英.利用Laplace变换求解分数阶Allen-Cahn方程[J].华侨大学学报(自然科学版),2020,41(4):549-554.DOI:10.11830/ISSN.1000-5013.201910013.
[2] QIAO Yuanyang,ZHAI Shuying,FENG Xinlong.An operator splitting method for image inpainting based on the Allen-Cahn equation[J].Chinese Journal of Engineering Mathematics,2018,35(6):722-732.DOI:10.3969/j.issn.1005-3085.2018.06.011.
[3] WHEELER A A,BOETTINGER W J,MCFADDEN G B.Phase-field model for isothermal phase transitions in binary alloys[J].Physical Review A,1992,45(10):7424-7439.DOI:10.1103/physreva.45.7424.
[4] CHEN Hao,SUN Haiwei.A dimensional splitting exponential time differencing scheme for multidimensional fractional Allen-Cahn equations[J].Journal of Scientific Computing,2021,87(1):30-55.DOI:10.1007/s10915-021-01431-0.
[5] LI Huanrong,SONG Zhengyuan.A reduced-order finite element method based on proper orthogonal decomposition for the Allen-Cahn model[J].Journal of Mathematical Analysis and Applications,2021,500(2):1261-1272.DOI:10.1016/j.jmaa.2021.125103.
[6] 王郭振.分数阶Allen-Cahn方程的有限元模拟及其理论分析[D].济南:山东师范大学,2020.
[7] 吴龙渊,汪精英,翟术英.求解二维Allen-Cahn方程的两种ADI格式[J].华侨大学学报(自然科学版),2019,40(3):412-420.DOI:10.11830/ISSN.1000-5013.201810014.
[8] 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):2449-2445.DOI:10.1016/j.cpc.2014.05.017.
[9] CHEN Wenping,LU Shujuan,HU Chen,et al.Crank-Nicolson Legendre spectral approximation for space-fractional Allen-Cahn equation[J].Electronic Journal of Differential Equations,2019,2019(76):1-17.
[10] KHALID N,ABBAS M,IQBAL M K,et al.A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions[J].Advances in Difference Equations,2020,2020(1):1-22.DOI:10.1186/s13662-020-02616-x.
[11] 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.DOI:10.11830/ISSN.1000-5013.201701004.
[12] CHEN Aimin,LIU Fawang.A finite volume unstructured mesh method for fractional-in-space Allen-Cahn equation[J].Chin Quart J of Math,2017, 32(4): 345-354.DOI:10.13371/j.cnki.chin.q.j.m.2017.04.002.
[13] LI Can,LIU Shuming.Local discontinuous Galerkin scheme for space fractional Allen-Cahn equation[J].Communications on Applied Mathematics and Computation,2020,2(1):73-91.DOI:10.1007/s42967-019-00034-9.
[14] WANG Guozhen,CHEN Huanzhen.Efficient implementation and numerical analysis of finite element method for fractional Allen-Cahn equation[J].Mathematical Problems in Engineering,2019(4):1-14.DOI:10.1155/2019/7969371.
[15] WENG Zhifeng,TANG Longkun.Analysis of the operator splitting scheme for the Allen-Cahn equation[J].Numerical Heat Transfer, Part B: Fundamentals,2016,70(5):472-483.DOI:10.1080/10407790.2016.1215714.
[16] ZHAI Shuying,WENG Zhifeng,FENG Xinlong.Fast explicit operator splitting method and time-step adaptivity for fractional non-local Allen-Cahn model[J].Applied Mathematical Modelling,2016,40(2):1315-1324.DOI:10.1016/j.apm.2015.07.021.
[17] CHEN Feng,SHEN Jie.Stability and error analysis of operator splitting methods for american options under the black-scholes model[J].Journal of Scientific Computing,2020,82(2):33-50.DOI:10.1007/s10915-020-01137-9.
[18] HAO Zhaopeng,ZHANG Zhongqiang,DU Rui.Fractional centered difference scheme for high-dimensional integral fractional Laplacian[J].Journal of Computational Physics,2021,424:109851.DOI:10.1016/j.jcp.2020.109851.
[19] STRANG G.On the construction and comparison of difference schemes[J].SIAM Journal of Numerical Analysis,1968,5(3):506-517.DOI:10.1137/0705041.

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备注/Memo

备注/Memo:
收稿日期: 2021-08-03
通信作者: 翟术英(1986-),女,副教授,博士,主要从事偏微分方程数值解的研究.E-mail:zhaishuying123456@163.com.
基金项目: 国家自然科学基金资助项目(11701196); 福建省自然科学基金资助项目(2020J01074)
更新日期/Last Update: 2022-11-20