Allen-Cahn方程的一种并行差分方法  

A Parallel Difference Method for Allen-Cahn Equation

作　　者：梁琪琪 全赛君 岳宏杰 韩丹夫 LIANG Qiqi;QUAN Saijun;YUE Hongjie;HAN Danfu(School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China;Department of Mathematics,Nantong Vocational University,Nangtong 226007,China)

机构地区：[1]杭州师范大学数学学院,浙江杭州311121 [2]南通职业大学数学教研室,江苏南通226007

出　　处：《杭州师范大学学报（自然科学版）》2024年第6期659-667,共9页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11471092);南通职业大学自然科学研究项目(23ZK07).

摘　　要：文章给出了具有纽曼边界条件的Allen-Cahn方程的交替分段Crank-Nicolson格式.结合经典Crank-Nicolson格式和4种不同类型的Saul‘yev非对称格式构造了ASC-N并行差分格式,对ASC-N格式的唯一性进行了理论分析,并讨论了数值算法的离散最大值原理.理论分析与数值结果表明,在网格密度较大时,ASC-N并行格式相较于经典的Crank-Nicolson格式可大幅度节省计算时间,高效求解Allen-Cahn方程.In this paper,the alternant-segmented Crank-Nicolson(ASC-N)scheme of Allen-Cahn equations with Newman boundary conditions was given.The ASC-N parallel difference scheme was constructed by combining the classic Crank-Nicolson scheme and four different Saul‘yev asymmetric schemes.The uniqueness of the ASC-N scheme was analyzed theoretically,and the discrete maximum principle of the numerical algorithm was discussed.Theoretical analysis and numerical results showed that the parallel ASC-N scheme could greatly save calculation time and efficiently solve Allen-Cahn equation compared with the classical Crank-Nicolson scheme when the grid density was high.

关 键 词：Allen-Cahn方程 ASC-N方法 离散最大值原理 并行差分格式 

分 类 号：O241.82[理学—计算数学] O246[理学—数学]