in solving problems in which time-dependent solution of the RT equation is important. The timestep however has to be very short because photons propagate at the speed of light unless a reduced speed of light approximation is employed.

In many astrophysical problems, for example cosmic reionization and galaxy formation, we have to deal with numerous radiation sources. [ @TRAPHIC introduced source merging procedure in order to avoid computationally expensive scaling with the number of sources and implemented it on Smoothed Particle Hydrodynamics (SPH). ]{} @START utilised the oct-tree algorithm [@tree] in order to accelerate the RT around point sources and they coupled the RT with SPH. In their method, distant sources from a target gas particle are grouped and regarded as a single point source when the angular size of the group of the sources is smaller than a critical value. Consequently, the effective number of radiation sources is largely reduced to $\log(N_{\rm s})$ when there are $N_{\rm s}$ sources.

The methods we explore in this paper are parallel to this approach except that we implement this grouping algorithm to grid-based codes. In one of our methods, we introduce supermeshes; a supermesh consists of $8^n$ meshes and it is characterised 