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

doi:10.1007/s10473-024-0215-y

Abstract

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

CLC Number:

65M12

Zhiyong SI. A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS[J].Acta mathematica scientia,Series B, 2024, 44(2): 650-670.

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