Adaptive mesh refinement approach to the construction of initial data for black hole collisions

The initial data for black hole collisions are constructed using a conforma l-imaging approach and a new adaptive mesh refinement technique, a fully th readed tree (FTT). We developed a second-order accurate approach to the sol ution of the constraint equations on a non-uniformly refined high-resolutio n Cartesian mesh including second-order accurate treatment of boundary cond itions at the black hole throats. FTT-based mesh refinement reduced memory and computer time requirements by several orders of magnitude compared to a uniform grid and allowed the construction of accurate initial data sets on Cartesian meshes. Test computations show quadratic convergence of the solu tions with increasing numerical resolution.