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Abstract Errors due to imperfect boundary conditions in numerical relativity simulations of binary black holes (BBHs) can produce unphysical reflections of gravitational waves which compromise the accuracy of waveform predictions, especially for subdominant modes. A system of higher order absorbing boundary conditions which greatly reduces this problem was introduced in earlier work (Buchman and Sarbach 2006Class. Quantum Grav.236709). In this paper, we devise two new implementations of this boundary condition system in the Spectral Einstein Code (SpEC), and test them in both linear multipolar gravitational wave and inspiralling mass ratio 7:1 BBH simulations. One of our implementations in particular is shown to be extremely robust and to produce accuracy superior to the standard freezing-Ψ₀boundary condition usually used bySpEC. 

SpECTRE is an open-source code for multi-scale, multi-physics problems in astrophysics and gravitational physics. In the future, we hope that it can be applied to problems across discipline boundaries in fluid dynamics, geoscience, plasma physics, nuclear physics, and engineering. It runs at petascale and is designed for future exascale computers. SpECTRE is being developed in support of our collaborative Simulating eXtreme Spacetimes (SXS) research program into the multi-messenger astrophysics of neutron star mergers, core-collapse supernovae, and gamma-ray bursts. 

Abstract Binary black holes are the most abundant source of gravitational-wave observations. Gravitational-wave observatories in the next decade will require tremendous increases in the accuracy of numerical waveforms modeling binary black holes, compared to today’s state of the art. One approach to achieving the required accuracy is using spectral-type methods that scale to many processors. Using theSpECTREnumerical-relativity (NR) code, we present the first simulations of a binary black hole inspiral, merger, and ringdown using discontinuous Galerkin (DG) methods. The efficiency of DG methods allows us to evolve the binary through ∼ 18 orbits at reasonable computational cost. We then useSpECTRE’s Cauchy Characteristic Evolution (CCE) code to extract the gravitational waves at future null infinity. The open-source nature ofSpECTREmeans this is the first time a spectral-type method for simulating binary black hole evolutions is available to the entire NR community.