(ed.). Gravitational waves (IOP, 2001)(422s).

362 Numerical relativityspite of more than 80 years of intense study, the solution space to the full set ofequations is essentially unknown. Most of what we know about this fundamentaltheory of physics has been gleaned from linearized solutions, highly idealizedsolutions possessing a high degree of symmetry (e.g., static, or spherically oraxially symmetric), or from perturbations of these solutions.Over the last several decades a growing research area, called numericalrelativity, has developed, where computers are employed to construct numericalsolutions to these equations. Although much has been learned through thisapproach, progress has been slow due to the complexity of the equations andinadequate computer power. For example, an important astrophysical applicationis the 3D spiralling coalescence of two black holes (BH) or neutron stars(NS), which will generate strong sources of gravitational waves. As has beenemphasized by Flanagan and Hughes, one of the best candidates for earlydetection by the laser interferometer network is increasingly considered to be BHmergers [3, 4]. The imminent arrival of data from the long awaited gravitationalwaveinterferometers (see, e.g., [3] and references therein) has provided a senseof urgency in understanding these strong sources of gravitational waves. Suchunderstanding can be obtained only through large-scale computer simulationsusing the full machinery of numerical relativity.Furthermore, the gravitational-wave signals are likely to be so weak by thetime they reach the detectors that reliable detection may be difficult without priorknowledge of the merger waveform. These signals can be properly interpreted, orperhaps even detected, only with a detailed comparison between the observationaldata and a set of theoretically determined ‘waveform templates’. In most cases,these waveform templates needed for gravitational-wave data analysis have tobe generated by large-scale computer simulations, adding to the urgency ofdeveloping numerical relativity. However, a realistic 3D simulation based on thefull Einstein equations is a highly non-trivial task—one can estimate the timerequired for a reasonably accurate 3D simulation of, say, the coalescence of acompact object binary, to be at least 100 000 Cray Y-MP hours!However, there is good reason for optimism that such problems can be solvedwithin the next decade. Scalable parallel computers, and efficient algorithms thatexploit them, are quickly revolutionizing computational science, and numericalrelativity is a great beneficiary of these developments. Over the last years thecommunity has developed 3D codes designed to solve the complete set of Einsteinequations that run very efficiently on large-scale parallel computers. We willdescribe below one such code, called ‘Cactus’, that has achieved 142 GFlops ona 1024 node Cray T3E-1200, which is more than 2000 times faster than 2D codesof a few years ago running on a Cray Y-MP (which also had only about 0.5%the memory capacity of the large T3E). Such machines are expected to scaleup rapidly as faster processors are connected together in even higher numbers,achieving Teraflop performance on real applications in a few years.Numerical relativity requires not only large computers and efficient codes,but also a wide variety of numerical algorithms for evolving and analysing