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A generalized scalar auxiliary variable method for the time-dependent Ginzburg-Landau equations

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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.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003, China

    Zhiyong Si

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  1. Zhiyong Si
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Correspondence to Zhiyong Si.

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Conflict of Interest The author declares no conflict of interest.

Additional information

This work was completed during the author’s visit to Peking University and supported by the National Natural Science Foundation of China (12126318, 12126302).

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Si, Z. A generalized scalar auxiliary variable method for the time-dependent Ginzburg-Landau equations. Acta Math Sci 44, 650–670 (2024). https://doi.org/10.1007/s10473-024-0215-y

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  • DOI: https://doi.org/10.1007/s10473-024-0215-y

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