This paper develops a generalized scalar auxiliary variable (SAV) method for the time-dependent Ginzburg-Landau equations. The backward Euler 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, which is confirmed by the numerical results. It shows that the numerical algorithm is stable.
翻译：本文为基于时间的 Ginzburg- Landau 方程式开发了通用的星标辅助变量(SAV) 方法。 后向的 Euler 用于分离基于时间的Ginzburg- Landau 方程式的时间衍生物。 在这个方法中, 系统是分解和线化的, 以避免在每一步都解决非线性方程式。 理论分析证明, 通用的SAV 方法可以保持最大约束原则和能源稳定性, 这一点得到数字结果的确认。 它表明数字算法是稳定的 。
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