Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method

TL;DR

This paper introduces a high-accuracy numerical code using Galerkin and Collocation spectral methods to solve the Bondi problem in axisymmetric vacuum spacetimes, enabling advanced gravitational wave studies.

Contribution

It is the first code employing Galerkin and Collocation spectral methods for the Bondi problem, demonstrating high accuracy and stability in numerical evolution of spacetimes.

Findings

Code achieves high accuracy and stability in tests

Spectral methods show promising convergence properties

Enables applications in gravitational wave evolution studies

Abstract

We present the first numerical code based on the Galerkin and Collocation methods to integrate the field equations of the Bondi problem. The Galerkin method like all spectral methods provide high accuracy with moderate computational effort. Several numerical tests were performed to verify the issues of convergence, stability and accuracy with promising results. This code opens up several possibilities of applications in more general scenarios for studying the evolution of spacetimes with gravitational waves.