  Vortex arrays in type-II superconductors admit the translational symmetry of
an infinite system. There are cases, however, like ultra-cold trapped Fermi
gases and the crust of neutron stars, where finite-size effects make it quite
more complex to account for the geometrical arrangement of vortices. Here, we
self-consistently generate these arrays of vortices at zero and finite
temperature through a microscopic description of the non-homogeneous superfluid
based on a differential equation for the local order parameter, obtained by
coarse graining the Bogoliubov-de Gennes (BdG) equations. In this way, the
strength of the inter-particle interaction is varied along the BCS-BEC
crossover, from largely overlapping Cooper pairs in the BCS limit to dilute
composite bosons in the BEC limit. Detailed comparison with two landmark
experiments on ultra-cold Fermi gases, aimed at revealing the presence of the
superfluid phase, brings out several features that makes them relevant for
other systems in nature as well.
