  We extend our recent unquenched ($N_f=2+1$ flavor) calculation of $B_K$ using
improved staggered fermions by including in the fits the finite volume shift
predicted by one-loop staggered chiral perturbation theory. The net result is
to lower the result in the continuum limit by 0.6%. This shift is slightly
smaller than our previous estimate of finite volume effects based on a direct
comparison between different volumes. To include the finite volume effects in a
reasonable time, we found it necessary to calculate them using Graphics
Processing Units.
