A NEW MIXED FORMULATION AND EFFICIENT NUMERICAL SOLUTION OF GINZBURG-LANDAU EQUATIONS UNDER THE TEMPORAL GAUGE

被引:17
作者
Gao, Huadong [1 ]
Sun, Weiwei [2 ]
机构
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[2] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
基金
中国国家自然科学基金;
关键词
Ginzburg-Landau equations; mixed formulation; fully linearized scheme; finite element methods; magnetic field; superconductivity; FINITE-ELEMENT METHODS; II SUPERCONDUCTORS; PARABOLIC EQUATIONS; MODEL; SIMULATION; FEM; APPROXIMATION; CONVERGENCE; BOUNDARY; DYNAMICS;
D O I
10.1137/15M1022744
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:A1339 / A1357
页数:19
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