The incorporation of radiative transfer effects into cosmological hydrodynamical simulations is essential for understanding how the intergalactic medium (IGM) makes the transition from a neutral medium to one that is almost fully ionized. Here, we present an approximate numerical method designed to study in a statistical sense how a cosmological density field is ionized by a set of discrete point sources. A diffuse background radiation field is also computed self-consistently in our procedure. The method requires relatively few time steps and can be employed with simulations having high resolution. We describe the details of the algorithm and provide a description of how the method can be applied to the output from a pre-existing cosmological simulation to study the systematic reionization of a particular ionic species. As a first application, we compute the reionization of He II by quasars in the range 3 ∼ < z ∼ < 6. PACS: 95.30.Jx; 98.80-
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