by the mean density of each chemical species of the meshes within the supermesh. Solving the RT on supermeshes whose angular size is similar to that of the group of the sources in question results in further reduction of computational time in principle. Another approach we take is the point source approximation, in which a group of sources sufficiently distant from a target mesh is treated as a point source. The latter can be regarded as a grid-based version of [START]{} [@START].

Unlike gravitational interactions to which the tree-algorithm has been widely applied, RT is affected by the medium between a source and a target. It is therefore very important to test these tree-based approaches in cases where an extended group of sources works as a powerful source in inhomogeneous medium and affects (e.g. ionizes) distant meshes. In this paper, we extensively investigate such cases in order to clarify advantages and disadvantages of the methods using tree-based algorithm.

This paper is organised as follows. In section 2, we describe the algorithm in detail. In section 3, we present several test problems and compare our methods to each other. We summarise and discuss the results in section 4.

Radiative transfer with 