Using hierarchical octrees in Monte Carlo radiative transfer simulations

A crucial aspect of 3D Monte Carlo radiative transferis the choice of the spatial gridused to partition the dustymedium. We critically investigate the use of octree gridsin Monte Carlo dust radiative transfer, with two different octreeconstruction algorithms (regular and barycentric subdivision) and three different octreetraversal algorithms (top-down, neighbour list, and the bookkeepingmethod). In general, regular octree gridsneed higher levels of subdivisioncompared to the barycentric gridsfor a fixed maximum cell mass threshold criterion. The total number of gridcells, however, depends on the geometry of the model. Surprisingly, regular octree gridsimulations turn out to be 10 to 20% more efficient in run time than the barycentric gridsimulations, even for those cases where the latter contain fewer gridcells than the former. Furthermore, we find that storing neighbour lists for each cell in an octree, ordered according to decreasing overlap area, is worth the additional memory and implementation overhead: using neighbour lists can cut down the gridtraversal by 20% compared to the traditional top-down method. In conclusion, the combination of a regular node subdivisionand the neighbour list method results in the most efficient octreestructure for Monte Carlo radiative transfersimulations.