  We study s-wave superconductivity in the two-dimensional square lattice
attractive Hubbard Hamiltonian for various inhomogeneous patterns of
interacting sites. Using the Bogoliubov-de Gennes (BdG) mean field
approximation, we obtain the phase diagram for inhomogeneous patterns in which
the on-site attractive interaction U_i between the electrons takes on two
values, U_i=0 and -U/(1-f) (with f the concentration of non-interacting sites)
as a function of average electron occupation per site n, and study the
evolution of the phase diagram as f varies. In certain regions of the phase
diagram, inhomogeneity results in a larger zero temperature average pairing
amplitude (order parameter) and also a higher superconducting (SC) critical
temperature T_c, relative to a uniform system with the same mean interaction
strength (U_i=-U on all sites). These effects are observed for stripes,
checkerboard, and even random patterns of the attractive centers, suggesting
that the pattern of inhomogeneity is unimportant. The phase diagrams also
include regions where superconductivity is obliterated due to the formation of
various charge ordered phases. The enhancement of T_{c} due to inhomogeneity is
robust as long as the electron doping per site n is less than twice the
fraction of interacting sites [2(1-f)] regardless of the pattern. We also show
that for certain inhomogeneous patterns, when n = 2(1-f), increasing
temperature can work against the stability of existing charge ordered phases
for large f and as a result, enhance T_{c}.

Superconductivity;Disordered Systems and Neural Networks