A Spectrally Accurate Algorithm and Analysis for a Ginzburg--Landau Model on Superconducting Surfaces

Ganesh, M.; Thompson, Ty

doi:10.1137/16m1096487

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2019

2024

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Cited by 6 publications

(1 citation statement)

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“…In [21], Li and Zhang proposed a decoupled and linearized FEM to solve the reformulated GL equations and presented error estimates in non-smooth domains. In [6], Ganesh and Thompson developed a time-space fully discrete implicit SMFEM algorithm for efficiently simulating the GL system modeling superconductivity on a class of superconducting surfaces. Wu and Sun [30] presented the analysis of linearized Galerkin FEMs for a mixed formulation of the time-dependent GL equations under the temporal gauge.…”

Section: Introductionmentioning

confidence: 99%

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

Si¹

2022

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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.

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Section: Introductionmentioning

confidence: 99%