In this effort, we form a new interdisciplinary team, comprised of computational mathematicans and astrophysicists, to focus on the development amd analysis of a new generation of simulation tools centered around spectral multi-domain methods. Initial tests have confirmed the potential of such techniques which, however, still require significant algorithmic developments, e.g., efficient nonlinear parallel elliptic solvers, stabilization techniques, and novel parallel temporal integration methods, to mature sufficiently. Simultaneously, attention will be paid to problems of a nature more specific to the Einstein equations, e.g., the initial data problem, control of constraint violating solutions, and suitable boundary conditions.
New urgency has been injected into numerical relativity and the development of computational methods for solving the Einstein equations by the current deployment of gravitational wave detectors, LIGO and, in the near future, LISA. To fully understand and analyze the signals measured with such facilities it is essential that a new generation of computational tools be available for solving the dynamical Einstein equations over very long times. In this interdiciplinary effort we combine expertize in computational mathematics and astrophysics to reach this goal, with the aim of modeling the full dynamics of a binary pair of black holes, conjectured to be a strong source of gravity waves as predicted by the general theory of relativity. Thus the effort will not only lead to the development of new computational simulation techniniques but also lead to the ability to test the validity some of the most fundamental physical theories known to mankind.
