Starting from a high-level problem description in terms of partial differential equations using abstract tensor notation, the Chemora framework discretizes, optimizes, and generates complete high performance codes for a wide range of compute architec
tures. Chemora extends the capabilities of Cactus, facilitating the usage of large-scale CPU/GPU systems in an efficient manner for complex applications, without low-level code tuning. Chemora achieves parallelism through MPI and multi-threading, combining OpenMP and CUDA. Optimizations include high-level code transformations, efficient loop traversal strategies, dynamically selected data and instruction cache usage strategies, and JIT compilation of GPU code tailored to the problem characteristics. The discretization is based on higher-order finite differences on multi-block domains. Chemoras capabilities are demonstrated by simulations of black hole collisions. This problem provides an acid test of the framework, as the Einstein equations contain hundreds of variables and thousands of terms.
The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produc
e numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binarys total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.
Suitable gauge conditions are fundamental for stable and accurate numerical-relativity simulations of inspiralling compact binaries. A number of well-studied conditions have been developed over the last decade for both the lapse and the shift and the
se have been successfully used both in vacuum and non-vacuum spacetimes when simulating binaries with comparable masses. At the same time, recent evidence has emerged that the standard Gamma-driver shift condition requires a careful and non-trivial tuning of its parameters to ensure long-term stable evolutions of unequal-mass binaries. We present a novel gauge condition in which the damping constant is promoted to be a dynamical variable and the solution of an evolution equation. We show that this choice removes the need for special tuning and provides a shift damping term which is free of instabilities in our simulations and dynamically adapts to the individual positions and masses of the binary black-hole system. Our gauge condition also reduces the variations in the coordinate size of the apparent horizon of the larger black hole and could therefore be useful when simulating binaries with very small mass ratios.
Generic inspirals and mergers of binary black holes produce beamed emission of gravitational radiation that can lead to a gravitational recoil or kick of the final black hole. The kick velocity depends on the mass ratio and spins of the binary as wel
l as on the dynamics of the binary configuration. Studies have focused so far on the most astrophysically relevant configuration of quasi-circular inspirals, for which kicks as large as 3,300 km/s have been found. We present the first study of gravitational recoil in hyperbolic encounters. Contrary to quasi-circular configurations, in which the beamed radiation tends to average during the inspiral, radiation from hyperbolic encounters is plunge dominated, resulting in an enhancement of preferential beaming. As a consequence, it is possible to achieve kick velocities as large as 10,000 km/s.
