  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.
