The RT is solved on the supermeshes at the lowest level, whose angular size is equal to or smaller than the angular size of the source group, $\theta_{\rm s}$. The supermeshes used are indicated by purple colour and their sizes are represented by the orange squares. []{data-label="fig:supermeshrt"}](fig3.eps){width="8.0cm"}

The computational cost by this method is expected to scale with $N_{\rm m}  \log(N_{\rm m}) \log(N_{\rm s}) $.

Point source approximation {#sec:start}
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Here we introduce another way of accelerating the RT calculation by using the oct-tree structure of the distribution of radiation sources. As in @START, we treat a group of sources in a tree node which satisfies the condition described by Eqn. (\[eq:opening\]) as a bright point source. Since we ignore the size of the source group, we solve the RT not on the supermeshes but on the meshes. Consequently, the computational cost scales with $N_{\rm m}^\frac{4}{3} \log(N_{\rm s})$. Although this is slightly more expensive computationally than the supermesh approximation in which the cost is proportional to $N_{\rm m} \log(N_{\rm m}) \log(N_{\rm s})$, this method may faster than the supermesh approximation for small $N_{\rm m}$ because we do not have to calculate ${\cal I}'_{00}$ and ${\cal I}'_{11}$ in the point source 