数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (2): 650-670.doi: 10.1007/s10473-024-0215-y

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A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

Zhiyong SI   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China
  • 收稿日期:2022-11-20 修回日期:2023-01-08 出版日期:2024-04-25 发布日期:2024-04-16
  • 作者简介:Zhiyong SI, E-mail: sizhiyong@hpu.edu.cn
  • 基金资助:
    National Natural Science Foundation of China (12126318, 12126302).

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

Zhiyong SI   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China
  • Received:2022-11-20 Revised:2023-01-08 Online:2024-04-25 Published:2024-04-16
  • About author:Zhiyong SI, E-mail: sizhiyong@hpu.edu.cn
  • Supported by:
    National Natural Science Foundation of China (12126318, 12126302).

摘要: This paper develops a generalized scalar auxiliary variable (SAV) method for the time-dependent Ginzburg-Landau equations. The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations. In this method, the system is decoupled and linearized to avoid solving the non-linear equation at each step. The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability, and this is confirmed by the numerical result, and also shows that the numerical algorithm is stable.

关键词: time-dependent Ginzburg-Landau equation, generalized scalar auxiliary variable algorithm, maximum bound principle, energy stability

Abstract: This paper develops a generalized scalar auxiliary variable (SAV) method for the time-dependent Ginzburg-Landau equations. The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations. In this method, the system is decoupled and linearized to avoid solving the non-linear equation at each step. The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability, and this is confirmed by the numerical result, and also shows that the numerical algorithm is stable.

Key words: time-dependent Ginzburg-Landau equation, generalized scalar auxiliary variable algorithm, maximum bound principle, energy stability

中图分类号: 

  • 65M12