求解二维Allen-Cahn方程的两种ADI格式  

Two ADI Schemes for Solving Two-Dimensional Alleb-Cahn Equations

作　　者：吴龙渊 汪精英 翟术英 WU Longyuan;WANG Jingying;ZHAI Shuying(School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2019年第3期412-420,共9页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(11701196);华侨大学中青年教师优秀青年科技创新人才项目(ZQN YX502);华侨大学研究生科研创新能力培养计划项目(1511422010)

摘　　要：为了构建二维Allen-Cahn方程的高效数值格式,利用算子分裂方法将原方程离散成非线性方程和二维热传导方程,其中,非线性方程有解析解.二维热传导方程时间离散采用Crank-Nicolson格式,空间离散分别采用二阶中心差分和四阶Padé逼近,得到两个稳定的数值格式.数值实验结果表明:格式具有有效性;能量呈现递减规律.Construct an efficient numerical scheme for the two-dimensional Allen-Cahn equation. The original equation is discretized into a nonlinear equation and a two-dimensional heat conduction equation by using the operator splitting method in which the nonlinear equation has an analytical solution. To the two-dimensional heat conduction equation, the time dispersion is in the Crank-Nicholson scheme, and the spatial discretization is obtained by using the second-order center difference and the fourth-order Padé approximation respectively, we two stable numerical schemes. Numerical experiments demonstrate the validity of the schemes and the law of energy diminution.

关 键 词：Allen-Cahn方程 算子分裂 交替方向隐格式 傅里叶分析 极大值原理 

分 类 号：O241.8[理学—计算数学]