Using hierarchical octrees in Monte Carlo radiative transfer simulations

TL;DR

This paper evaluates different octree grid construction and traversal algorithms in 3D Monte Carlo radiative transfer, finding that regular octrees with neighbour lists offer the best efficiency improvements.

Contribution

It provides a comparative analysis of octree construction and traversal methods, identifying the most efficient combination for radiative transfer simulations.

Findings

Regular octrees need more subdivision levels than barycentric ones.

Regular octrees are 10-20% faster in run time than barycentric grids.

Using neighbour lists reduces grid traversal time by 20%.

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.