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Here we report a developed high performance and simplified version of thecode denominated RIO, which can be easily extended, for the generalized BSSNformulation. We implement a code which is regular at the center of symmetry,without use a special procedure for regularization, as usual. We getexponential convergence for constraints. The numerical algorithm is based onthe Galerkin-Collocation method developed successfully for diverse physicalscenarios by the Numerical Relativity Group at UERJ. For the sake of clarity inpresentation, we consider here the most simple case to display the most salientfeatures of the procedure. Thus, we focus on the definite tests of the newnumerical framework. The timing and performance of the code show that we canreach a better accuracy close to the machine precision, for the Hamiltonian andmomentum constraints. RIO will be an open source code; currently is undercontinuous development to consider more general and realistic problems.

New numerical framework for the generalized Baumgarte-Shapiro-Shibata-Nakamura formulation: The vacuum case for spherical symmetry