We present convergent gravitational waveforms extracted fromthree-dimensional, numerical simulations in the wave zone and with causallydisconnected boundaries. These waveforms last for multiple periods and are veryaccurate, showing a peak error to peak amplitude ratio of 2% or better. Ourapproach includes defining the Weyl scalar Psi_4 in terms of a three-plus-onedecomposition of the Einstein equations; applying, for the first time, a novelalgorithm due to Misner for computing spherical harmonic components of our wavedata; and using fixed mesh refinement to focus resolution on non-linear sourceswhile simultaneously resolving the wave zone and maintaining a causallydisconnected computational boundary. We apply our techniques to a (linear)Teukolsky wave, and then to an equal mass, head-on collision of two blackholes. We argue both for the quality of our results and for the value of theseproblems as standard test cases for wave extraction techniques.
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