ARGOT: Accelerated radiative transfer on grids using oct-tree

Abstract

We present two types of numerical prescriptions that accelerate the radiative transfer calculation around point sources within a three-dimensional Cartesian grid by using the oct-tree structure for the distribution of radiation sources. In one prescription, distant radiation sources are grouped as a bright extended source when the group's angular size, ${\theta }_{\mathrm{s}}$, is smaller than a critical value, ${\theta }_{\mathrm{crit}}$, and radiative transfer is solved on supermeshes whose angular sizes are similar to that of the group of sources. The supermesh structure is constructed by coarse-graining the mesh structure. With this method, the computational time scales with $N_{\mathrm{m}}\log (N_{\mathrm{m}})\log (N_{\mathrm{s}})$ where $N_{\mathrm{m}}$ and $N_{\mathrm{s}}$ are the number of meshes and that of radiation sources, respectively. While this method is very efficient, it inevitably overestimates the optical depth when a group of sources acts as an extended powerful radiation source and affects distant meshes. In the other prescription, a distant group of sources is treated as a bright point source ignoring the spatial extent of the group and the radiative transfer is solved on the meshes rather than the supermeshes. This prescription is simply a grid-based version of {\scriptsize START} by Hasegawa & Umemura and yields better results in general with slightly more computational cost ($\propto N_{\mathrm{m}}^{4/3}\log (N_{\mathrm{s}})$) than the supermesh prescription. Our methods can easily be implemented to any grid-based hydrodynamic codes and are well-suited to the adaptive mesh refinement methods.

13 pages, 12 figures, submitted to MNRAS. Revised according to referee's comments

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