Using hierarchical octrees in Monte Carlo radiative transfer simulations
  A crucial aspect of 3D Monte Carlo radiative transfer is the choice of the
spatial grid used to partition the dusty medium. We critically investigate the
use of octree grids in Monte Carlo dust radiative transfer, with two different
octree construction algorithms (regular and barycentric subdivision) and three
different octree traversal algorithms (top-down, neighbour list, and the
bookkeeping method). In general, regular octree grids need higher levels of
subdivision compared to the barycentric grids for a fixed maximum cell mass
threshold criterion. The total number of grid cells, however, depends on the
geometry of the model. Surprisingly, regular octree grid simulations turn out
to be 10 to 20% more efficient in run time than the barycentric grid
simulations, even for those cases where the latter contain fewer grid cells
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 grid traversal by 20% compared to the traditional top-down method. In
conclusion, the combination of a regular node subdivision and the neighbour
list method results in the most efficient octree structure for Monte Carlo
radiative transfer simulations.
