is hence proportional to the number of sources. In the next subsection, we will describe the method to decrease the effective number of radiation sources by using the oct-tree structure.

Source grouping algorithm
-------------------------

As in @START, we construct the oct-tree structure for the distribution of radiation sources. A cubic computational domain is hierarchically subdivided into 8 cubic cells until each cell contains only one radiation source or the size of a cell becomes sufficiently small compared to that of the computational domain. We call these sub-volumes ‘tree nodes’. When the side length of the cubic computational domain is $L$, the width of a level $l$ tree node is given by $w^{(l)} = L/2^{l}$. Each tree node records the centre of the luminosity of the radiation sources contained in the node, $${\boldsymbol  r } = \frac{\sum_m {\boldsymbol  r }_m L_m}{\sum_m L_m}, 
\label{eq:centre}$$ and the total luminosity, $$L = \sum_m L_m,  
\label{eq:totallum}$$ where ${\boldsymbol  r }_m$ and $L_m$ indicate the position vector and the luminosity of a radiation source, respectively, and subscript $m$ runs over all sources within the tree node.

Once we have constructed the tree structure, we loop over all meshes. RT from all the radiation sources to each 