A new ray-tracing scheme for 3D diffuse radiation transfer on highly
  parallel architectures
  We present a new numerical scheme to solve the transfer of diffuse radiation
on three-dimensional mesh grids which is efficient on processors with highly
parallel architecture such as recently popular GPUs and CPUs with multi- and
many-core architectures. The scheme is based on the ray-tracing method and the
computational cost is proportional to $N_{\rm m}^{5/3}$ where $N_{\rm m}$ is
the number of mesh grids, and is devised to compute the radiation transfer
along each light-ray completely in parallel with appropriate grouping of the
light-rays. We find that the performance of our scheme scales well with the
number of adopted CPU cores and GPUs, and also that our scheme is nicely
parallelized 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 for
the angular resolution of our ray-tracing scheme, we perform several numerical
simulations of the photo-ionization of neutral hydrogen gas by ionizing
radiation sources without the "on-the-spot" approximation, in which the
transfer of diffuse radiation by radiative recombination is incorporated in a
self-consistent manner.
