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

TL;DR

This paper introduces a high-performance, simplified numerical framework called RIO for the generalized BSSN formulation in spherical symmetry, achieving exponential convergence and high accuracy without special regularization procedures.

Contribution

The paper presents a new, efficient numerical code for the generalized BSSN formulation that is regular at the center of symmetry and demonstrates exponential convergence and high precision.

Findings

Exponential convergence for constraints achieved

High accuracy close to machine precision

Code is regular at the symmetry center without special procedures

Abstract

Here we report a developed high performance and simplified version of the code denominated RIO, which can be easily extended, for the generalized BSSN formulation. We implement a code which is regular at the center of symmetry, without use a special procedure for regularization, as usual. We get exponential convergence for constraints. The numerical algorithm is based on the Galerkin-Collocation method developed successfully for diverse physical scenarios by the Numerical Relativity Group at UERJ. For the sake of clarity in presentation, we consider here the most simple case to display the most salient features of the procedure. Thus, we focus on the definite tests of the new numerical framework. The timing and performance of the code show that we can reach a better accuracy close to the machine precision, for the Hamiltonian and momentum constraints. RIO will be an open source code; currently is under continuous development to consider more general and realistic problems.