  We describe a method for evolving the projected Gross-Pitaevskii equation
(PGPE) for an interacting Bose gas in a harmonic oscillator potential, with the
inclusion of a long-range dipolar interaction. The central difficulty in
solving this equation is the requirement that the field is restricted to a
small set of prescribed modes that constitute the low energy c-field region of
the system. We present a scheme, using a Hermite-polynomial based spectral
representation, that precisely implements this mode restriction and allows an
efficient and accurate solution of the dipolar PGPE. We introduce a set of
auxiliary oscillator states to perform a Fourier transform necessary to
evaluate the dipolar interaction in reciprocal space. We extensively
characterize the accuracy of our approach, and derive Ehrenfest equations for
the evolution of the angular momentum.
