As a network of advanced-era gravitational wave detectors is nearing its design sensitivity, efficient and accurate waveform modeling becomes more and more relevant. Understanding of the nature of the signal being sought can have an order unity effect on the event rates seen in these instruments. The paper provides a description of key elements of the Spectral Einstein Code ({tt SpEC}), with details of our spectral adaptive mesh refinement (AMR) algorithm that has been optimized for binary black hole (BBH) evolutions. We expect that the gravitational waveform catalog produced by our code will have a central importance in both the detection and parameter estimation of gravitational waves in these instruments.
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