Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge (Communications in Computational Physics, 2019)
In this paper, a new numerical scheme for the time dependent Ginzburg-Landau (GL) equations under the Lorentz gauge is proposed. We first rewrite theoriginal GL equations into a new mixed formulation, which consists of three parabolicequations 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 elementmethod is used in spatial discretization. The new approach offers many advantageson both accuracy and efficiency over existing methods for the GL equations underthe Lorentz gauge. Three physical variables ψ, σ and θ can be solved accurately anddirectly. More importantly, the new approach is well suitable for non-convex superconductors. We present a set of numerical examples to confirm these advantages.