Rio: A new computational framework for accurate initial data of binary black holes

We present a computational framework (Rio) in the ADM 3+1 approach for numerical relativity. This work enables us to carry out high resolution calculations for initial data of two arbitrary black holes. We use the transverse conformal treatment, the Bowen-York and the puncture methods. For the numerical solution of the Hamiltonian constraint we use the domain decomposition and the spectral decomposition of Galerkin-Collocation. The nonlinear numerical code solves the set of equations for the spectral modes using the standard Newton-Raphson method, LU decomposition and Gaussian quadratures. We show the convergence of the Rio code. This code allows for easy deployment of large calculations. We show how the spin of one of the black holes is manifest in the conformal factor.