[1]崔晨,吴哲,翟术英.非局部守恒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(5):698-704.[doi:10.11830/ISSN.1000-5013.202107008]
　CUI Chen,WU Zhe,ZHAI Shuying.Effective Operator Splitting Scheme for Conservative Nonlocal Allen-Cahn Equation[J].Journal of Huaqiao University(Natural Science),2022,43(5):698-704.[doi:10.11830/ISSN.1000-5013.202107008]
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非局部守恒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5期
页码:
698-704
栏目:
出版日期:
2022-09-13

文章信息/Info

Title:
Effective Operator Splitting Scheme for Conservative Nonlocal Allen-Cahn Equation
文章编号:
1000-5013(2022)05-0698-07
作者:
崔晨;  吴哲;  翟术英
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
CUI Chen;  WU Zhe;  ZHAI Shuying
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
非局部Allen-Cahn方程;  拉格朗日乘子;  算子分裂方法;  质量守恒
Keywords:
nonlocal Allen-Cahn equation;  Lagrange multiplier;  operator splitting method;  mass conservation
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.202107008
文献标志码:
A
摘要:
研究带有拉格朗日乘子的非局部守恒Allen-Cahn方程的高效算子分裂格式.基于算子分裂思想,将原方程分解为非线性方程、非局部方程和拉格朗日乘子方程;然后,利用非线性方程解析求解,非局部方程结合矩形公式及Crank-Nicolson格式建立二阶差分格式,利用拉格朗日乘子方程进行数值积分离散.理论分析表明:数值格式满足质量守恒.最后,通过数值算例验证算法的有效性,包括收敛阶、能量递减及质量守恒.
Abstract:
An effective operator splitting scheme for solving the nonlocal Allen-Cahn equation with a Lagrange multiplier is studied, based on the operator splitting method, the original equation is discretized respectively into a nonlinear equation, a nonlocal equation and a Lagrange multiplier equation. Then, the nonlinear equation is solved analytically; the nonlocal equation is discreted using rectangle formula and Crank-Nicolson format, and Lagrange multiplier equation is discreted using trapezoidal formulas. The theoretical results show that the proposed scheme satisfies is mass conservation. Numerical experiments demonstrate the validity of the proposed method, including convergence order, energy decline and mass conservation.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2021-07-06
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及理论的研究.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: 2022-09-20