  In order to understand the rate of merger of stellar-mass black hole binaries
(BHBs) by gravitational wave (GW) emission it is important to determine the
major pathways to merger. We use numerical simulations to explore the evolution
of BHBs inside the radius of influence of supermassive black holes (SMBHs) in
galactic centers. In this region the evolution of binaries is dominated by
perturbations from the central SMBH. In particular, as first pointed out by
Antonini and Perets, the Kozai-Lidov (KL) mechanism trades relative inclination
of the BHB to the SMBH for eccentricity of the BHB, and for some orientations
can bring the BHB to an eccentricity near unity. At very high eccentricities,
GW emission from the BHB can become efficient, causing the members of the BHB
to coalesce. We use a novel combination of two N-body codes to follow this
evolution. We are forced to simulate small systems to follow the behavior
accurately. We have completed 400 simulations that range from $\sim$ 300 stars
around a $10^{3}$ M$_{\odot}$ black hole to $\sim$ 4500 stars around a $10^{4}$
M$_{\odot}$ black hole. These simulations are the first to follow the internal
orbit of a binary near a SMBH while also following the changes to its external
orbit self-consistently. We find that this mechanism could produce mergers at a
maximum rate per volume of $\sim 100$ Gpc$^{-3}$ yr$^{-1}$ or considerably less
if the inclination oscillations of the binary remain constant as the BHB
inclination to the SMBH changes, or if the binary black hole fraction is small.
