Using hierarchical octrees in Monte Carlo radiative transfer simulations

Abstract

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.

High-resolution, 3D radiative transfer modeling

“…SKIRT can furthermore be applied to model the emission of simulated galaxies from hydrodynamical simulations (Camps et al 2013a). An important extension of SKIRT in view of high-resolution radiative transfer models involves the implementation of adaptive grid structures such as the hierarchical Octree (Kurosawa & Hillier 2001;Niccolini & Alcolea 2006), k-d grid structures, and Voronoi tesselations (Voronoi 1908), which are described in more detail in Saftly et al (2013Saftly et al ( , 2014 and Camps et al (2013b), respectively. Such adaptive grid structures allow to increase the resolution in the dust grid where dust clumps or asymmetric spiral arm structures are present, and at the same time keep the computational cost limited.…”

Hierarchical octree andk-d tree grids for 3D radiative transfer simulations

“…The construction algorithm for the k-d tree is completely analogous to the technique we used for the construction of the octree grid structure in SKIRT, as explained in Saftly et al (2013). The tree is represented as a list of nodes that starts with the cuboidal root node.…”

“…Another option could be to split the cell such that the two subnodes have equal mass. This option is similar to the barycentric subdivision in octree grids explored by Saftly et al (2013), but, contrary to octrees, it is possible to achieve exact equal-mass splitting for k-d trees. A third option is to choose the splitting location such that the two subnodes have equal mean density.…”

“…The most important step in the grid traversal process is to determine the next cell along the path which contains the exit position from the previous cell. Saftly et al (2013) investigated in great detail three possible algorithms for this step in the context of octree grids. It was found that a neighbour list search method is very fast and efficient and beats the traditional top-down method (Glassner 1984).…”

“…In Saftly et al (2013), we presented a detailed investigation of how hierarchical octrees are used in Monte Carlo dust radiative transfer. We investigated different methods of setting up an octree (using either regular or barycentric subdivision of the nodes) and different methods of traversing the tree, and showed that the combination of regular node subdivision and neighbour list search is the most efficient method for calculating paths through an octree.…”