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Volume 22, Issue 1
Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge

Huadong Gao

DOI: 10.4208/cicp.OA-2016-0120

Commun. Comput. Phys., 22 (2017), pp. 182-201.

Published online: 2019-10

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  • 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.

  • Keywords

Ginzburg-Landau equations, Lorentz gauge, fully linearized scheme, FEMs, magnetic field, electric potential, superconductivity.

  • AMS Subject Headings

65M12, 65M22, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huadong@hust.edu.cn (Huadong Gao)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-22-182, author = {Gao , Huadong}, title = {Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge}, journal = {Communications in Computational Physics}, year = {2019}, volume = {22}, number = {1}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0120}, url = {http://global-sci.org/intro/article_detail/cicp/13352.html} }
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 -

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.

Gao , Huadong. (2019). Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge. Communications in Computational Physics. 22 (1). 182-201. doi:10.4208/cicp.OA-2016-0120
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