Radiative transfer on hierarchial grids

Context. Continuum radiative-transfer simulations are necessary for the interpretation of observations of dusty astrophysical objects and for relating the results of magnetohydrodynamical simulations to observations. The calculations are computationally difficult, and simulations of objects with high optical depths in particular require considerable computational resources. Aims. Our aim is to show how radiative transfer calculations on adaptive three-dimensional grids can be accelerated. Methods. We show how the hierarchial tree structure of the model can be used in the calculations. 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. Results. An adaptive model of the molecular cloud with fewer than 8% of the cells in the uniform grid produces results in good agreement with the full resolution model. The relative root-mean-square (rms) error of the surface brightness is less than or similar to 4% at all wavelengths, and in regions of high column density the relative rms error is only similar to 10(-4). Computation with the adaptive model is faster by a factor of similar to 5. Our new method for calculating the scattered flux is faster by a factor of about four 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 is 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 of low mean density.