A Fast, Accurate, and Robust Algorithm for Transferring Radiation in Three‐dimensional Space

We have developed an algorithm for transferring radiation inthree-dimensional space. The algorithm computes radiation source and sink termsusing the Fast Fourier Transform (FFT) method, based on a formulation in whichthe integral of any quantity (such as emissivity or opacity) over any volumemay be written in the classic convolution form. The algorithm is fast with thecomputational time scaling as N (log N)^2, where N is the number of grid pointsof a simulation box, independent of the number of radiation sources.Furthermore, in this formulation one can naturally account for both localradiation sources and diffuse background as well as any extra external sources,all in a self-consistent fashion. Finally, the algorithm is completely stableand robust. While the algorithm is generally applicable, we test it on a set of problemsthat encompass a wide range of situations in cosmological applications,demonstrating that the algorithm is accurate. These tests show that thealgorithm produces results that are in excellent agreement with analyticexpectations in all cases. In particular, radiation flux is guaranteed topropagate in the right direction, with the ionization fronts traveling at thecorrect speed with an error no larger than one cell for all the cases tested.The total number of photons is conserved in the worst case at 10% level andtypically at 1-5% level over hundreds of time steps. As an added advantage, theaccuracy of the results depends weakly on the size of the time step, with atypical cosmological hydrodynamic time step being sufficient.Comment: submitted to ApJ, 50 pages, added comparisons to ray tracing metho