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Simulating vortex motion in superconducting films with the time-dependent Ginzburg-Landau equations. (English) Zbl 0904.65127

Summary: The time-dependent Ginzburg-Landau equations model a thin-film superconductor of finite size placed under a magnetic field. For numerical computation, we use a staggered grid discretization, a technique well known in numerical fluid mechanics. Some properties of the solutions are established. An efficient explicit-implicit method based on the forward Euler method is developed. In our simulations, we impose natural boundary conditions at the edge of the superconductor. With suitable choices of parameters (corresponding to physical superconductors of type II) and the strength of the external magnetic field, the steady-state solutions exhibit vortices. When a variable strength magnetic field, simulating a transient current, is introduced, we observe motion of the vortices in a periodic pattern.

MSC:

65Z05 Applications to the sciences
35Q72 Other PDE from mechanics (MSC2000)
65N06 Finite difference methods for boundary value problems involving PDEs
82D55 Statistical mechanics of superconductors
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