Despite the simple dynamics of the two-body problem in Newtonian gravity, the relativistic problem is notoriously difficult. Gravitational radiation gradually removes energy and angular momentum from the system, driving the objects to inspiral together until they merge. The predictions of Einstein’s quadrupole formula were confirmed with the 1974 Nobel-prize observation of radiative decay in the Hulse-Taylor binary pulsar. In 2015, the first direct GW observations by LIGO allowed us to probe strong-field, highly dynamical processes from black hole mergers, and neutron star merger observations are expected next. Because the detector’s output contains noise greater than the signal itself, match-filtering is typically necessary, which requires a priory theoretical knowledge of the gravitational-wave signal. Accurate waveform templates are essential for the identification and physical interpretation of their sources, and considerable effort has been made to model the two-body dynamics in the strong-field regime of general relativity. Although analytical techniques, based on perturbative approximations, have been very successful in modelling early inspiral, their limit of applicability is reached when strong-field nonlinear effects appear. Numerical relativity thus becomes crucial for modelling the system through late inspiral, plunge, merger and beyond and calculating the resulting waveforms.

Efforts to obtain numerical solutions for black hole binaries date back to the 1960s and 1970s. NCSA was founded in 1976 by Larry Smarr, motivated by the problem of simulating a binary black hole collision. The Cactus code (E. Seidel, G. Allen et al., AEI, NCSA, Cardiff, LSU) targeted systematized the effort towards solving this problem since 1998. These efforts started to pay off in 2001 (M. Alcubierre, B. Brügmann, E. Seidel et al. 3D Grazing Collision of Two Black Holes, PRL 87 27) and were followed in 2005 by the breakthrough of F. Pretorius (Evolution of Binary Black-Hole Spacetimes, PRL 95), whence the first successful simulations were performed, initiating an era of rapid developments in numerical relativity and the theoretical discovery of several unexpected strong-field phenomena.