  We investigate the effect of a ferromagnetic dot on a thin-film
superconductor. We use a real-space method to solve the linearized
Ginzburg-Landau equation in order to find the upper critical field, H_c_3. We
show that H_c_3 is crucially dependent on dot composition and geometry, and may
be significantly greater than H_c_2. H_c_3 is maximally enhanced when (1) the
dot saturation magnetization is large, (2) the ratio of dot thickness to dot
diameter is of order one, and (3) the dot thickness is large.
