  Ground-state properties of a two-dimensional system of superconducting
vortices in the presence of a periodic array of strong pinning centers are
studied analytically and numerically. The ground states of the vortex system at
different filling ratios are found using a simple geometric argument under the
assumption that the penetration depth is much smaller than the spacing of the
pin lattice. The results of this calculation are confirmed by numerical studies
in which simulated annealing is used to locate the ground states of the vortex
system. The zero-temperature equilibrium magnetization as a function of the
applied field is obtained by numerically calculating the energy of the ground
state for a large number of closely spaced filling ratios. The results show
interesting commensurability effects such as plateaus in the B-H diagram at
simple fractional filling ratios.
