Year: 2017
Author: Huadong Gao
Communications in Computational Physics, Vol. 22 (2017), Iss. 1 : pp. 182–201
Abstract
In this paper, a new numerical scheme for the time dependent Ginzburg-Landau (GL) equations under the Lorentz gauge is proposed. We first rewrite the original GL equations into a new mixed formulation, which consists of three parabolic equations for the order parameter ψ, the magnetic field σ=curlA, the electric potential θ=divA and a vector ordinary differential equation for the magnetic potential A, respectively. Then, an efficient fully linearized backward Euler finite element method (FEM) is proposed for the mixed GL system, where conventional Lagrange element method is used in spatial discretization. The new approach offers many advantages on both accuracy and efficiency over existing methods for the GL equations under the Lorentz gauge. Three physical variables ψ, σ and θ can be solved accurately and directly. More importantly, the new approach is well suitable for non-convex superconductors. We present a set of numerical examples to confirm these advantages.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2016-0120
Communications in Computational Physics, Vol. 22 (2017), Iss. 1 : pp. 182–201
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Ginzburg-Landau equations Lorentz gauge fully linearized scheme FEMs magnetic field electric potential superconductivity.
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