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We present a method to construct semi-numerical ``simulations'', which canefficiently generate realizations of halo distributions and ionization maps athigh redshifts. Our procedure combines an excursion-set approach withfirst-order Lagrangian perturbation theory and operates directly on the lineardensity and velocity fields. As such, the achievable dynamic range with ouralgorithm surpasses the current practical limit of N-body codes by orders ofmagnitude. This is particularly significant in studies of reionization, wherethe dynamic range is the principal limiting factor. We test our halo-findingand HII bubble-finding algorithms independently against N-body simulations withradiative transfer and obtain excellent agreement. We compute the sizedistributions of ionized and neutral regions in our maps. We find even largerionized bubbles than do purely analytic models at the same volume-weighted meanhydrogen neutral fraction. We also generate maps and power spectra of 21-cmbrightness temperature fluctuations, which for the first time includecorrections due to gas bulk velocities. We find that velocities widen the tailsof the temperature distributions and increase small-scale power, though theseeffects quickly diminish as reionization progresses. We also include somepreliminary results from a simulation run with the largest dynamic range todate: a 250 Mpc box that resolves halos with masses M >~ 2.2 x10^8 M_sun. Weshow that accurately modeling the late stages of reionization requires suchlarge scales. The speed and dynamic range provided by our semi-numericalapproach will be extremely useful in the modeling of early structure formationand reionization.

Efficient Simulations of Early Structure Formation and Reionization