  We use numerical minimization of a model free energy functional to study the
effects of columnar pinning centers on the structure and thermodynamics of a
system of pancake vortices in the mixed phase of highly anisotropic layered
superconductors. The magnetic field and the columnar pins are assumed to be
perpendicular to the layers. Our methods allow us to study in detail the
density distribution of vortices in real space. We present results for the
dependence of the average number of vortices trapped at a pinning center on
temperature and pinning strength, and for the effective interaction between
nearby pinned vortices arising from short-range correlations in the vortex
liquid. For a commensurate, periodic array of pinning centers, we find a line
of first order vortex lattice melting transitions in the temperature $T$ vs.
pin concentration $c$ plane, which terminates at an experimentally accessible
critical point as $c$ is increased. Beyond this point, the transition is
replaced by a crossover. Our results should also apply, with little change, to
thin-film superconductors with strong point pinning.
