摘要
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 parameterψ,the magnetic fieldσ=curlA,the electric potentialθ=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 variablesψ,σandθcan 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.
基金
The work of the author was supported in part by a grant from the National Natural Science Foundation of China(NSFC)under grant No.11501227
Fundamental Research Funds for the Central Universities,HUST,China,under Grant No.2014QNRC025,No.2015QN13.The author would like to thank Dr.Kui Du for useful suggestions.
