Paper Info
Title
A New Mixed Formulation and Efficient Numerical Solution of Ginzburg-Landau Equations Under the Temporal Gauge.
Abstract
In this paper, we present a new numerical approach to the time-dependent Ginzburg-Landau (GL) equations under the temporal gauge ( zero electric potential gauge). The approach is based on a mixed formulation of the GL equations, which consists of two parabolic equations for the order parameter psi and the magnetic field sigma = curl A, respectively, and a vector ordinary differential equation for the magnetic potential A. A fully linearized Galerkin finite element method is presented for solving the mixed GL system. The new approach offers many advantages on both accuracy and efficiency over existing methods. In particular, the equations for psi and sigma are uniformly parabolic and, therefore, the method provides optimal-order accuracy for the two physical components psi and sigma. Since in the temporal direction, a fully linearized backward Euler scheme is used for psi and sigma and a forward Euler scheme is used for A, respectively, the system is fully decoupled and at each time step, the three variables psi, sigma, and A can be solved simultaneously. Moreover, we present numerical comparisons with two commonly used Galerkin methods for the GL equations under the temporal gauge and the Lorentz gauge, respectively. Our numerical results show that the new approach requires fewer iterations for solving the linear systems arising at each time step and the computational cost for the vector ODE seems neglectable. Several numerical examples in both two-and three-dimensional spaces are investigated.
Year
DOI
Venue
2016
10.1137/15M1022744
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
Ginzburg-Landau equations,mixed formulation,fully linearized scheme,finite element methods,magnetic field,superconductivity
Parabolic partial differential equation,Mathematical optimization,Ordinary differential equation,Mathematical analysis,Finite element method,Magnetic potential,Gauge (firearms),Curl (mathematics),Backward Euler method,Mathematics,Parabola
Journal
Volume
Issue
ISSN
38
3
1064-8275
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Huadong Gao1455.89
Weiwei Sun215415.12