In this thesis, we present a novel algorithm for computing the radiation field in astrophysical simulations. The algorithm is tree-based, similar to many gravity solvers, and allows computation of radiative transfer in O(Nsink logNsource) in cases without absorption, and O(Nsink logNsource logN) time with absorption. The algorithm scales well with the number of processors due to its tree-based nature, and is highly tunable in accuracy and speed. It is also only weakly dependent on both the energy band and the number of energy bands used. We provide a suite of tests of the code showing its ability to create accurate fluxes, ionization fronts, hydrodynamics coupling, and shadowing. We apply the algorithm in a set of simulations on an isolated spiral galaxy from the AGORA project. The algorithm is used to calculate FUV fields within the galaxy, which self-consistently sets the dominant photoelectric heating in the gas. This has never before been performed in galaxy simulations. We find, in agreement with Ostriker et al. [2010], that FUV can be a very important regulation mechanism for star formation in a galaxy. Depending on the assumed opacity, FUV can decrease the average star formation rate (SFR) anywhere from 15% to a factor of twenty. We compare this regulation mechanism to a highly effective model of supernovae (SNe) feedback, which reduces the SFR by a factor of twenty as well. However, SNe feedback destroys most of the gas structure in the process, whereas FUV has minimal impact on the gas structure. In the simulations with FUV radiation, we are also able to create a two phase medium that is a function of the mean FUV intensity the gas receives. Finally, we find that simulations with FUV agree well with observations of nearby spirals on the Kennicutt-Schmidt relation, at least at gas surface densities of 0.2 - 30 M⊙. At surface densities higher than 30 M⊙, we find that FUV is not an effective regulator which is consistent with arguments that SNe or other feedback mechanisms should become the primary regulator. / Thesis / Doctor of Philosophy (PhD)