We present new methods for radiative transfer on hierarchial grids. We
develop a new method for calculating the scattered flux that employs the grid
structure to speed up the computation. We describe a novel subiteration
algorithm that can be used to accelerate calculations with strong dust
temperature self-coupling. We compute two test models, a molecular cloud and a
circumstellar disc, and compare the accuracy and speed of the new algorithms
against existing methods. An adaptive model of the molecular cloud with less
than 8 % of the cells in the uniform grid produced results in good agreement
with the full resolution model. The relative RMS error of the surface
brightness <4 % at all wavelengths, and in regions of high column density the
relative RMS error was only 10^{-4}. Computation with the adaptive model was
faster by a factor of ~5. The new method for calculating the scattered flux is
faster by a factor of ~4 in large models with a deep hierarchy structure, when
images of the scattered light are computed towards several observing
directions. The efficiency of the subiteration algorithm is highly dependent on
the details of the model. In the circumstellar disc test the speed-up was a
factor of two, but much larger gains are possible. The algorithm is expected to
be most beneficial in models where a large number of small, dense regions are
embedded in an environment with a lower mean density.Comment: Accepted to A&A; 13 pages, 8 figures; (v2: minor typos corrected
