Spectral Characteristic Evolution: A New Algorithm for Gravitational Wave Propagation

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.

28 pages, 9 figures

References in corpus (2)

• The Magnus expansion and some of its applications
• Fast and Exact Spin-s Spherical Harmonic Transforms

Cited by in corpus (2)

• Extraction of Gravitational Waves in Numerical Relativity
• Characteristic Formulation for Metric $f(R)$ Gravity