  We present results from a large volume simulation of Hydrogen reionization.
We combine 3d radiative transfer calculations and an N-body simulation,
describing structure formation in the intergalactic medium, to detail the
growth of HII regions around high redshift galaxies. Our simulation tracks
1024^3 dark matter particles, in a box of co-moving side length 65.6 Mpc/h.
This large volume allows us to accurately characterize the size distribution of
HII regions throughout most of the reionization process. At the same time, our
simulation resolves many of the small galaxies likely responsible for
reionization. It confirms a picture anticipated by analytic models: HII regions
grow collectively around highly-clustered sources, and have a well-defined
characteristic size, which evolves from a sub-Mpc scale at the beginning of
reionization to R > 10 Mpc towards the end. We present a detailed statistical
description of our results, and compare them with a numerical scheme based on
the analytic model by Furlanetto, Zaldarriaga, and Hernquist. We find that the
analytic calculation reproduces the size distribution of HII regions and the 21
cm power spectrum of the radiative transfer simulation remarkably well. The
ionization field from the simulation, however, has more small scale structure
than the analytic calculation, owing to Poisson scatter in the simulated
abundance of galaxies on small scales. We propose and validate a simple scheme
to incorporate this scatter into our calculations. Our results suggest that
analytic calculations are sufficiently accurate to aid in predicting and
interpreting the results of future 21 cm surveys. In particular, our fast
numerical scheme is useful for forecasting constraints from future 21 cm
surveys, and in constructing mock surveys to test data analysis procedures.
