The Bondi problem revisited: a spectral domain decomposition code

TL;DR

This paper introduces a stable, efficient spectral domain decomposition code for solving the Bondi problem, demonstrating exponential convergence and applications to mass decay and waveform extraction at null infinity.

Contribution

It develops a novel Galerkin-Collocation based domain decomposition method for the Bondi problem, combining stability, efficiency, and high convergence.

Findings

Exponential convergence of the numerical method.

Observation of Bondi mass decay in nonlinear regime.

Successful extraction of wave-forms at null infinity.

Abstract

We present a simple domain decomposition code based on the Galerkin-Collocation method to integrate the field equations of the Bondi problem. The algorithm is stable, exhibits exponential convergence when considering the Bondi formula as an error measure, and is computationally economical. We have incorporated features of both Galerkin and Collocation methods along with the establishment of two non-overlapping subdomains. We have further applied the code to show the decay of the Bondi mass in the nonlinear regime and its power-law late time decay. Another application is the determination of the wave-forms at the future null infinity connected with distinct initial data.