Giant Steps in Cefalu
  Giant steps is a technique to accelerate Monte Carlo radiative transfer in optically-thick cells of astrophysical atmospheres by greatly reducing the number of Monte Carlo steps needed to propagate photon packets through such cells. Giant steps replaces the exact diffusion treatment of ordinary Monte Carlo radiative transfer in the cells by an approximate diffusion treatment. In this paper, we describe the basic idea of giant steps and report demonstration giant-steps flux calculations for the grey atmosphere. Speed-up factors of order 100 are obtained relative to ordinary Monte Carlo radiative transfer. In practical applications, speed-up factors of order ten (Mazzali et al. 2001) and perhaps more are possible. The speed-up factor is likely to be significantly application-dependent and there is a trade-off between speed-up and accuracy. This paper and past work (Mazzali et al. 2001) suggest that giant-steps error can probably be kept to a few percent by using sufficiently large boundary-layer optical depths while still maintaining large speed-up factors. Thus, giant steps can be characterized as a moderate accuracy radiative transfer technique. 
David J. Jeffery & Paolo A. Mazzali