FRG: Collaborative Research: Developing Spectral Methods for Numerical Solutions of the Einstein Equations

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In this effort, we form a new interdisciplinary team, comprised ofcomputational 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 techniqueswhich, however, still require significant algorithmic developments,e.g., efficient nonlinear parallel elliptic solvers, stabilizationtechniques, and novel parallel temporal integration methods, to maturesufficiently. Simultaneously, attention will be paid to problems of anature more specific to the Einstein equations, e.g., the initial dataproblem, control of constraint violating solutions, and suitableboundary conditions.New urgency has been injected into numerical relativity and thedevelopment of computational methods for solving the Einsteinequations by the current deployment of gravitational wave detectors,LIGO and, in the near future, LISA. To fully understand and analyzethe signals measured with such facilities it is essential that a newgeneration of computational tools be available for solving the dynamical Einstein equations over very long times. In this interdiciplinaryeffort we combine expertize in computational mathematics andastrophysics to reach this goal, with the aim of modeling the fulldynamics of a binary pair of black holes, conjectured to be a strongsource of gravity waves as predicted by the general theory of relativity.Thus the effort will not only lead to the development of newcomputational simulation techniniques but also lead to the abilityto test the validity some of the most fundamental physical theoriesknown to mankind.