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

388 Numerical relativity18.5 Computational science, numerical relativity, and the‘Cactus’ code18.5.1 The computational challenges of numerical relativityBefore we describe our computational methods in the following subsections, wesummarize the computational challenges of numerical relativity discussed above.It is in response to these challenges that we have devised the computationalmethods.• Computational challenges due to the complexity of the physics involved.The Einstein equations are probably the most complex partial differentialequations in all physics, forming a system of dozens of coupled, nonlinearequations, with thousands of terms, of mixed hyperbolic, elliptic, and evenundefined types in a general coordinate system. The evolution has ellipticconstraints that should be satisfied at all times. In simulations withoutsymmetry, as would be the case for realistic astrophysical processes, codescan involve hundreds of 3D arrays, and ten of thousands of operationsper grid point per update. Moreover, for simulations of astrophysicalprocesses, we will ultimately need to integrate numerical relativity withtraditional tools of computational astrophysics, including hydrodynamics,nuclear astrophysics, radiation transport and magnetohydrodynamics, whichgovern the evolution of the source terms (i.e. the right-hand side) of theEinstein equations. This complexity requires us to push the frontiers ofmassively parallel computation.• Challenge in collaborative technology. The integration of numerical relativityinto computational astrophysics is a multidisciplinary development,partly due to the complexity of the Einstein equations, and partly due to thephysical systems of interest. Solving the Einstein equations on massivelyparallel computers involves gravitational physics, computational science, numericalalgorithm and applied mathematics. Furthermore, for the numericalsimulations of realistic astrophysical systems; many physics disciplines,including relativity, astrophysics, nuclear physics, and hydrodynamics areinvolved. It is therefore essential to have the numerical code software engineeredto allow codevelopment by different research groups and groups withdifferent expertise.• The multiscale problem. Astrophysics of strongly gravitating systemsinherently involves many length and timescales. The microphysics of theshortest scale (the nuclear force), controls macroscopic dynamics on thestellar scale, such as the formation and collapse of neutron stars (NSs). Onthe other hand, the stellar scale is at least ten times less than the wavelengthof the gravitational waves emitted, and many orders of magnitude less thanthe astronomical scales of their accretion disk and jets; these larger scalesprovide the directly observed signals. Numerical studies of these systems,aiming at direct comparison with observations, fundamentally require the