N_{\rm s}$ for the transfer from point sources. Its known disadvantage is the inability to track collimated radiation fields and hence the inability to cast sharp shadows owing to the numerical diffusion.

The methods whose computational cost is similar to that of the short characteristics method with small loss of accuracy compared to the long characteristics method have also been developed (@razoumov05 and ‘authentic RT’ by Nakamoto et al. in @iliev06). Adaptive ray tracing [@abel02] has been widely used for RT around point sources [@wise11].

Mote Carlo transport [@ciardi01] is also straight forward. The advantage of this approach is that comparatively few approximations to the RT equations need to be made. The resulting radiation field however inevitably becomes noisy [see @iliev06] due to its stochastic nature unless a huge number of photon packets are transported. This method is computationally very expensive in the optically thick regime.

The methods, which consider the moments of the RT equations and consist in choosing a closure relation to solve them, can lead to substantial simplifications that can drastically speed up the calculations because its computational cost scales with $\sim N_{\rm m}$. The most common of these methods is the flux-limited diffusion, which solves the 