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

2022/10/16 by Zhiyong Si, Si, Zhiyong
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2210.08425

openalex publication_date 2022/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Time - dependent Ginzburg - Landau approach and application to superconductivity
• An energy stable and maximum bound principle preserving scheme for the dynamic Ginzburg-Landau equations under the temporal gauge
• Variable coefficient complex Ginzburg-Landau equation
• Efficient simulation of complex Ginzburg--Landau equations using high-order exponential-type methods
• Error analysis of scalar auxiliary variable finite element methods for the Landau–Lifshitz–Bloch equation