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We present a new numerical scheme to solve the transfer of diffuse radiationon three-dimensional mesh grids which is efficient on processors with highlyparallel architecture such as recently popular GPUs and CPUs with multi- andmany-core architectures. The scheme is based on the ray-tracing method and thecomputational cost is proportional to $N_{\rm m}^{5/3}$ where $N_{\rm m}$ isthe number of mesh grids, and is devised to compute the radiation transferalong each light-ray completely in parallel with appropriate grouping of thelight-rays. We find that the performance of our scheme scales well with thenumber of adopted CPU cores and GPUs, and also that our scheme is nicelyparallelized on a multi-node system by adopting the multiple wave front scheme,and the performance scales well with the amount of the computational resources.As numerical tests to validate our scheme and to give a physical criterion forthe angular resolution of our ray-tracing scheme, we perform several numericalsimulations of the photo-ionization of neutral hydrogen gas by ionizingradiation sources without the "on-the-spot" approximation, in which thetransfer of diffuse radiation by radiative recombination is incorporated in aself-consistent manner.

A new ray-tracing scheme for 3D diffuse radiation transfer on highly parallel architectures