含平均曲率项的修正Allen-Cahn方程的高效算子分裂方法

曹子涵; 吴哲; 翟术英

doi:10.21656/1000-0887.460107

含平均曲率项的修正Allen-Cahn方程的高效算子分裂方法

doi: 10.21656/1000-0887.460107

华侨大学数学科学学院, 福建泉州 362021

基金项目:

国家自然科学基金(11701196)

数学与信息网络教育部重点实验室（北京邮电大学）开放课题（KF202606）

详细信息

作者简介:
曹子涵(2001—), 男, 硕士生(E-mail: caozihan163163@163.com);吴哲(1991—), 女, 实验师, 硕士(E-mail: WUzhe33@hqu.edu.cn);翟术英(1986—), 女, 教授, 博士(通信作者. E-mail: zsy@hqu.edu.cn).

通讯作者:
翟术英(1986—), 女, 教授, 博士(通信作者. E-mail: zsy@hqu.edu.cn).

中图分类号: O357.41
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- 文章访问数: 9
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出版历程
- 收稿日期: 2025-05-29
- 修回日期: 2025-07-30
- 网络出版日期: 2026-07-23

An Efficient Operator Splitting Method for Modified Allen-Cahn Equations With Mean Curvature Terms

School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P.R. China

Funds:

The National Science Foundation of China(11701196)

摘要

摘要: 含平均曲率项的修正Allen-Cahn方程可有效模拟与曲率相关的物理过程,但非线性项和梯度模的存在导致难以构造高效求解格式.该文提出了一种求解此模型的高效数值格式.基于Strang算子分裂方法,在时间方向上将原方程分解为三个子方程: 非线性方程解析求解；平均曲率方程采用二阶Runge-Kutta方法结合中心差分建立全离散显格式；热传导方程采用Crank-Nicolson格式离散求解,并构造交替方向隐式(ADI)快速求解策略.理论分析表明，构造格式具有二阶收敛精度.最后,通过数值算例验证格式收敛阶和有效性.
- 修正Allen-Cahn方程 /
- 算子分裂格式 /
- ADI /
- 收敛性分析
Abstract: The modified Allen-Cahn equation with the mean curvature source term can effectively model curvature-driven physical processes. However, the nonlinear term and gradient magnitude make it difficult to design efficient numerical schemes. An efficient numerical scheme was proposed for solving the equation. Based on the Strang operator splitting method, the original equation was discretized in time into three subproblems: the nonlinear equation was solved analytically; the mean curvature equation was discretized using the second-order Runge-Kutta method combined with central differences to establish a fully discrete explicit scheme, while the heat equation was discretized with the Crank-Nicolson method and solved via the alternating direction implicit (ADI) fast scheme. Theoretical analysis shows that, the proposed scheme achieves second order convergence accuracy. Finally, numerical experiments were presented to validate the convergence rate and effectiveness of the scheme.
- modified Allen-Cahn equation /
- operator splitting scheme /
- ADI /
- convergence analysis

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参考文献(33)

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含平均曲率项的修正Allen-Cahn方程的高效算子分裂方法

doi: 10.21656/1000-0887.460107

作者简介:
曹子涵(2001—), 男, 硕士生(E-mail: caozihan163163@163.com);吴哲(1991—), 女, 实验师, 硕士(E-mail: WUzhe33@hqu.edu.cn);翟术英(1986—), 女, 教授, 博士(通信作者. E-mail: zsy@hqu.edu.cn).

通讯作者:
翟术英(1986—), 女, 教授, 博士(通信作者. E-mail: zsy@hqu.edu.cn).

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An Efficient Operator Splitting Method for Modified Allen-Cahn Equations With Mean Curvature Terms

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目录

留言板

含平均曲率项的修正Allen-Cahn方程的高效算子分裂方法

doi: 10.21656/1000-0887.460107

作者简介: 曹子涵(2001—), 男, 硕士生(E-mail: caozihan163163@163.com);吴哲(1991—), 女, 实验师, 硕士(E-mail: WUzhe33@hqu.edu.cn);翟术英(1986—), 女, 教授, 博士(通信作者. E-mail: zsy@hqu.edu.cn).

通讯作者: 翟术英(1986—), 女, 教授, 博士(通信作者. E-mail: zsy@hqu.edu.cn).

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出版历程

An Efficient Operator Splitting Method for Modified Allen-Cahn Equations With Mean Curvature Terms

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出版历程

目录

作者简介:
曹子涵(2001—), 男, 硕士生(E-mail: caozihan163163@163.com);吴哲(1991—), 女, 实验师, 硕士(E-mail: WUzhe33@hqu.edu.cn);翟术英(1986—), 女, 教授, 博士(通信作者. E-mail: zsy@hqu.edu.cn).

通讯作者:
翟术英(1986—), 女, 教授, 博士(通信作者. E-mail: zsy@hqu.edu.cn).