| This thesis is a compilation of numerical studies into the behavior of magnetic vortices in the type-II superconductors, both without defects and in the presence of defects. A highly effective numerical method of solution of the time-dependent Ginzburg-Landau equations is developed. The numerical solution of the TDGL equations reveals the behavior and structure of the vortex state in fine detail. The results of the computational models agree well with experiment. A wide range of phenomena is studied: the Meissner effect, the entrance of vortices in the bulk of the superconductor, the equilibrium Abrikosov lattice, hysteresis, surface barrier, vortex-antivortex annihilation and magnetic field reversal, the effects of transport current, interaction with various defects, both natural and artificial---twin boundaries, lattices of point and finite-size defects, as well as more exotic phenomena: symmetry breaking, dimensional phase transitions in thin films, and single vortex generators. The developed technique and code base allows for a thorough and accurate modeling of the real-world phenomena in type-II superconductors, as well as design of exotic pinning structures to achieve the desired material characteristics for practical development of high-field superconductors. |
