TY - JOUR
T1 - Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge
AU - Gao , Huadong
JO - Communications in Computational Physics
VL - 1
SP - 182
EP - 201
PY - 2019
DA - 2019/10
SN - 22
DO - http://doi.org/10.4208/cicp.OA-2016-0120
UR - https://global-sci.org/intro/article_detail/cicp/13352.html
KW - Ginzburg-Landau equations, Lorentz gauge, fully linearized scheme, FEMs, magnetic field, electric potential, superconductivity.
AB - <p style="text-align: justify;">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=curl<strong>A</strong>, the electric potential θ=div<strong>A</strong> and a vector ordinary differential equation for the magnetic potential <strong>A</strong>,
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.</p>