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The initial data for black hole collisions are 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. 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 solutions with increasing numerical resolution.

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Classical and Quantum Gravity

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