Spectral Characteristic Evolution: A New Algorithm for Gravitational Wave Propagation

TL;DR

This paper introduces a spectral algorithm for solving Einstein's equations in gravitational wave modeling, achieving significant efficiency improvements and enabling more accurate waveform extraction.

Contribution

The paper presents a novel spectral characteristic evolution algorithm within the SpEC framework, enhancing stability, convergence, and computational efficiency for gravitational wave simulations.

Findings

Algorithm demonstrates stability and convergence.

Achieves two orders of magnitude speedup.

Provides gauge-invariant waveforms for astrophysical simulations.

Abstract

We present a spectral algorithm for solving the full nonlinear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate spectral characteristic evolution as a technical precursor to Cauchy Characteristic Extraction (CCE), a rigorous method for obtaining gauge-invariant gravitational waveforms from existing and future astrophysical simulations. We demonstrate the new algorithm's stability, convergence, and agreement with existing evolution methods. We explain how an innovative spectral approach enables a two orders of magnitude improvement in computational efficiency.