  In this paper, we propose a new finite element approach to simulate the
time-dependent Ginzburg-Landau equations under the temporal gauge, and design
an efficient preconditioner for the Newton iteration of the resulting discrete
system. The new approach solves the magnetic potential in H(curl) space by the
lowest order of the second kind Nedelec element. This approach offers a simple
way to deal with the boundary condition, and leads to a stable and reliable
performance when dealing with the superconductor with reentrant corners. The
comparison in numerical simulations verifies the efficiency of the proposed
preconditioner, which can significantly speed up the simulation in large-scale
computations.
