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

This paper develops a generalized scalar auxiliary variable (SAV) method for the time-dependent Ginzburg-Landau equations. The backward Euler is used for discretiz-ing 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.