Numerical relaxation approach for solving the general Ginzburg-Landau equations for type-II superconductors

A numerical relaxation approach for solving the general Ginzburg-Landau equations for type-II superconductors is developed. It is first applied to an isotropic type-II superconductor near ${\mathit{H}}_{\mathrm{c}1\mathrm{}}$ in order to establish the reliability and effectiveness of this approach. The strength of this approach should be in dealing with anisotropic and/or inhomogeneous systems. As an initial test of this strength, we have applied it to some anisotropic cases. Distributions of the superconducting order parameter and the local magnetic field, as well as the lower critical field for these cases, are presented.