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Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge

Part of:Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  03 May 2017

Huadong Gao
Huadong Gao*
Affiliation:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R. China
*
*Corresponding author. Email address:huadong@hust.edu.cn (H. Gao)

Abstract

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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.

Keywords

Ginzburg-Landau equationsLorentz gaugefully linearized schemeFEMsmagnetic fieldelectric potentialsuperconductivity

MSC classification

Secondary:65M12: Stability and convergence of numerical methods65M22: Solution of discretized equations65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 1 , July 2017, pp. 182 - 201
Copyright
Copyright © Global-Science Press 2017 

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