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

Summary 399these techniques are used to extend the ability of the community to handle theearlier orbital phase, it will be important to have an understanding of details ofthis most violent phase in advance, both as a testbed to ensure that results arecorrect, and because the understanding we gain may be useful in devising theappropriate techniques for longer-term evolution.18.8 SummaryIn this article we have attempted to review the essential mathematical andcomputational elements needed for a full-scale numerical relativity code thatcan treat a variety of problems in relativistic astrophysics and gravitation.Various formulations of the Einstein equations for evolving spacelike time slices,techniques for providing initial data, the basic ideas of gauge conditions, severalimportant analysis tools for discovering the physics contained in a simulation,and the numerical algorithms for each of these items have been reviewed.Unfortunately, we have only been able to cover the basics of such a program,and in addition many promising alternative approaches have necessarily been leftout.As one can see, the solution to a single problem in numerical relativityrequires a huge range of computational and mathematical techniques. It is trulya large-scale effort, involving experts in computer and computational science,mathematical relativity, astrophysics, and so on. For these reasons, aided bycollaborations such as the NSF Black Hole Grand Challenge Alliance and theNCSA/Potsdam/Wash U collaboration, there has been a great focusing of effortover the last years.A natural byproduct of this focusing has been the development of codesthat are used and extended by large groups. A code must have a large arsenalof modules at its disposal: different initial data sets, gauge conditions, horizonfinders, slicing conditions, waveform extraction, elliptic equation solvers, AMRsystems, boundary modules, different evolution modules, etc. Furthermore,these codes must run efficiently on the most advanced supercomputers available.Clearly, the development of such a sophisticated code is beyond any single personor group. In fact, it is beyond the capability of a single community! Differentresearch communities, from computer science, physics and astrophysics, mustwork together to develop such a code.As an example of such a project, the ‘Cactus’ code has been developedby a large international collaboration [133, 134]. This code is an outgrowthof the last decade of 3D numerical relativity development primarily atNCSA/Potsdam/Wash U, and builds heavily on the experience gained indeveloping previous generation codes [34, 45, 148]. Cactus has a verymodular structure, allowing different physics, analysis, and computational sciencemodules to be plugged in. In fact, versions of essentially all the modules listedabove are already developed for the code. For example, several formulations