  The initial data for black hole collisions is constructed using a
conformal-imaging approach and a new adaptive mesh refinement technique, a
fully threaded tree (FTT). We developed a second-order accurate approach to the
solution of the constraint equations on a non-uniformly refined high resolution
Cartesian mesh including second-order accurate treatment of boundary conditions
at the black hole throats. Results of test computations show convergence of the
solution as the numerical resolution is increased. FTT-based mesh refinement
reduces the required memory and computer time by several orders of magnitude
compared to a uniform grid. This opens up the possibility of using Cartesian
meshes for very high resolution simulations of black hole collisions.
