Vortex dynamics in superconductors with periodic pinning arrays

We apply the periodic time-dependent Ginzburg-Landau (TDGL) model to type-II superconductors with periodic pinning arrays. A pinning array can pin vortices regularly and periodically, and shapes various vortex lattices depending on the applied magnetic fields. At the matching fields, vortex lattices are commensurate with defect lattices, and the pinning effects are enhanced. The results are consistent with those obtained by considering large-scale simulated annealing as well as flux-gradient-driven molecular dynamics