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.
Publication Source (Journal or Book title)
Classical and Quantum Gravity
Diener, P., Jansen, N., Khokhlov, A., & Novikov, I. (2000). Adaptive mesh refinement approach to the construction of initial data for black hole collisions. Classical and Quantum Gravity, 17 (2), 435-451. https://doi.org/10.1088/0264-9381/17/2/312