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

TL;DR

This paper introduces a generalized scalar auxiliary variable method for the time-dependent Ginzburg-Landau equations, ensuring stability and maximum bound principle preservation through decoupling and linearization techniques.

Contribution

It develops a novel generalized SAV method that simplifies computations while maintaining stability and physical bounds for the equations.

Findings

The method preserves maximum bound principle.

The method ensures energy stability.

Numerical results confirm stability and effectiveness.

Abstract

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.