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

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

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.

Author Details

Huadong Gao

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