Detailed theoretical studies of the high-redshift universe , and especially reionization , are generally forced to rely on time-consuming N-body codes and/or approximate radiative transfer algorithms .
We present a method to construct semi-numerical “ simulations ” , which can efficiently generate realizations of halo distributions and ionization maps at high redshifts .
Our procedure combines an excursion-set approach with first-order Lagrangian perturbation theory and operates directly on the linear density and velocity fields .
As such , the achievable dynamic range with our algorithm surpasses the current practical limit of N-body codes by orders of magnitude .
This is particularly significant in studies of reionization , where the dynamic range is the principal limiting factor because ionized regions reach scales of tens of comoving Mpc .
We test our halo-finding and ionization-mapping algorithms separately against N-body simulations with radiative transfer and obtain excellent agreement .
We compute the size distributions of ionized and neutral regions in our maps .
We find even larger ionized bubbles than do purely analytic models at the same volume-weighted mean hydrogen neutral fraction , \bar { x } _ { HI } , especially early in reionization .
We also generate maps and power spectra of 21-cm brightness temperature fluctuations , which for the first time include corrections due to gas bulk velocities .
We find that velocities widen the tails of the temperature distributions and increase small-scale power , though these effects quickly diminish as reionization progresses .
We also include some preliminary results from a simulation run with the largest dynamic range to date : a 250 Mpc box that resolves halos with masses M \geq 2.2 \times 10 ^ { 8 } M _ { \odot } .
We show that accurately modeling the late stages of reionization , \bar { x } _ { HI } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt% \hbox { $ < $ } } 0.5 , requires such large scales .
The speed and dynamic range provided by our semi-numerical approach will be extremely useful in the modeling of early structure formation and reionization .