  We have performed fully self-consistent $N$-body simulations of star clusters
near the Galactic center (GC). Such simulations have not been performed because
it is difficult to perform fast and accurate simulations of such systems using
conventional methods. We used the Bridge code, which integrates the parent
galaxy using the tree algorithm and the star cluster using the fourth-order
Hermite scheme with individual timestep. The interaction between the parent
galaxy and the star cluster is calculate with the tree algorithm. Therefore,
the Bridge code can handle both the orbital and internal evolutions of star
clusters correctly at the same time. We investigated the evolution of star
clusters using the Bridge code and compared the results with previous studies.
We found that 1) the inspiral timescale of the star clusters is shorter than
that obtained with "traditional" simulations, in which the orbital evolution of
star clusters is calculated analytically using the dynamical friction formula
and 2) the core collapse of the star cluster increases the core density and
help the cluster survive. The initial conditions of star clusters is not so
severe as previously suggested.
