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SAV/重心插值配点法求解Allen-Cahn方程

黄蓉 邓杨芳 翁智峰

黄蓉, 邓杨芳, 翁智峰. SAV/重心插值配点法求解Allen-Cahn方程[J]. 机械工程学报, 2023, 44(5): 573-582. doi: 10.21656/1000-0887.430149
引用本文: 黄蓉, 邓杨芳, 翁智峰. SAV/重心插值配点法求解Allen-Cahn方程[J]. 机械工程学报, 2023, 44(5): 573-582. doi: 10.21656/1000-0887.430149
HUANG Rong, DENG Yangfang, WENG Zhifeng. The SAV Scheme Based on the Barycentric Interpolation Collocation Method for the Allen-Cahn Equation[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 44(5): 573-582. doi: 10.21656/1000-0887.430149
Citation: HUANG Rong, DENG Yangfang, WENG Zhifeng. The SAV Scheme Based on the Barycentric Interpolation Collocation Method for the Allen-Cahn Equation[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 44(5): 573-582. doi: 10.21656/1000-0887.430149

SAV/重心插值配点法求解Allen-Cahn方程

doi: 10.21656/1000-0887.430149
基金项目: 

国家自然科学基金项目(11701197)

中央高校基本科研业务费(ZQN702)

详细信息
    作者简介:

    黄蓉(1995—),女,硕士生(E-mail: hraccount@163.com);邓杨芳(1997—),女,硕士生(E-mail: hqudeng@163.com);翁智峰(1985—),男,副教授(通讯作者. E-mail: zfwmath@163.com).

    通讯作者:

    翁智峰(1985—),男,副教授(通讯作者. E-mail: zfwmath@163.com).

  • 中图分类号: O241.82

The SAV Scheme Based on the Barycentric Interpolation Collocation Method for the Allen-Cahn Equation

Funds: 

The National Natural Science Foundation of China(11701197)

  • 摘要: 采用标量辅助变量(scalar auxiliary variable, SAV)方法结合重心插值配点法求解二维Allen-Cahn方程.在时间方向上分别采用Crank-Nicolson格式、二阶向后差分格式离散,空间方向上采用重心Lagrange插值配点法离散,建立了两种无条件能量稳定SAV格式,并给出了重心插值配点格式的逼近性质.数值实验表明:两种SAV配点格式的时间收敛阶为二阶,并满足能量递减规律.与空间采用有限差分法离散对比,重心Lagrange 配点格式具有指数收敛的特性.

     

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出版历程
  • 收稿日期:  2022-04-27
  • 修回日期:  2022-06-11
  • 刊出日期:  2023-05-31

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