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.
@article{arxiv.1406.7029,
title = {Spectral Characteristic Evolution: A New Algorithm for Gravitational Wave Propagation},
author = {Casey J. Handmer and Béla Szilágyi},
journal= {arXiv preprint arXiv:1406.7029},
year = {2015}
}