The incorporation of radiative transfer effects into cosmological hydrodyna
mical simulations is essential for understanding how the intergalactic medi
um (IGM) makes the transition from a neutral medium to one that is almost f
ully ionized. Here, we present an approximate numerical method designed to
study in a statistical sense, how a cosmological density field is ionized b
y a set of discrete point sources. A diffuse background radiation field is
also computed self-consistently in our procedure. The method requires relat
ively few time steps and can be employed with simulations having high resol
ution. We describe the details of the algorithm and provide a description o
f how the method can be applied to the output from a pre-existing cosmologi
cal simulation to study the systematic reionization of a particular ionic s
pecies. As a first application, we compute the reionization of He II by qua
sars in the range 3 less than or similar to z less than or similar to 6. (C
) 2001 Elsevier Science B.V. All rights reserved.