Galerkin-Collocation domain decomposition method for arbitrary binary black holes

TL;DR

This paper introduces a new spectral method framework for high-resolution initial data calculations of arbitrary binary black holes in numerical relativity, utilizing domain decomposition and spectral techniques.

Contribution

It develops a novel Galerkin-collocation domain decomposition approach for binary black holes, enabling precise initial data computation with spectral methods in numerical relativity.

Findings

Convergence demonstrated for conformal factor and ADM mass.

Features of the conformal factor analyzed for various black hole parameters.

High-resolution initial data generation for arbitrary binary black holes achieved.

Abstract

We present a new computational framework for the Galerkin-collocation method for double domain in the context of ADM 3+1 approach in numerical relativity. This work enables us to perform high resolution calculations for initial sets of two arbitrary black holes. We use the Bowen-York method for binary systems and the puncture method to solve the Hamiltonian constraint. 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 convergence of our code for the conformal factor and the ADM mass. Thus, we display features of the conformal factor for different masses, spins and linear momenta.