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

Abstract

Context. A crucial ingredient for numerically solving the three-dimensional radiative transfer problem is the choice of the grid that discretizes the transfer medium. Many modern radiative transfer codes, whether using Monte Carlo or ray tracing techniques, are equipped with hierarchical octree-based grids to accommodate a wide dynamic range in densities. Aims. We critically investigate two different aspects of octree grids in the framework of Monte Carlo dust radiative transfer. Inspired by their common use in computer graphics applications, we test hierarchical k-d tree grids as an alternative for octree grids. On the other hand, we investigate which node subdivision-stopping criteria are optimal for constructing of hierarchical grids. Methods. We implemented a k-d tree grid in the 3D radiative transfer code SKIRT and compared it with the previously implemented octree grid. We also considered three different node subdivision-stopping criteria (based on mass, optical depth, and density gradient thresholds). Based on a small suite of test models, we compared the efficiency and accuracy of the different grids, according to various quality metrics. Results. For a given set of requirements, the k-d tree grids only require half the number of cells of the corresponding octree. Moreover, for the same number of grid cells, the k-d tree is characterized by higher discretization accuracy. Concerning the subdivision stopping criteria, we find that an optical depth criterion is not a useful alternative to the more standard mass threshold, since the resulting grids show a poor accuracy. Both criteria can be combined; however, in the optimal combination, for which we provide a simple approximate recipe, this can lead to a 20% reduction in the number of cells needed to reach a certain grid quality. An additional density gradient threshold criterion can be added that solves the problem of poorly resolving sharp edges and strong density gradients. Conclusions. We advocate the use of k-d trees and the proposed combination of criteria to set up hierarchical grids for 3D radiative transfer. These recipes are straightforward for implementing and should help to develop faster and more accurate 3D radiative transfer codes.

SKIRT: An advanced dust radiative transfer code with a user-friendly architecture

“…However, while an octree forces all eight subcells to be created at the same time, a k-d tree allows more fine-grained control over which of the two initial subcells are subdivided further. As reported in Saftly et al (2014), this property gives kd tree grids a relevant advantage over octree grids in the context of Fig. 4.…”

High-resolution, 3D radiative transfer modelling

“…The code is designed in a way that it can take into account all relevant physical processes such as scattering, absorption, and thermal re-emission by dust, for a wide variety of environments. SKIRT is equipped with a large collection of possible geometries and geometry decorators , efficient grid structures (Saftly et al , 2014Camps et al 2013), and hybrid parallelisation techniques (Verstocken et al 2017).…”

Trust

“…The code handles multiple dust mixtures and arbitrary 3D geometries for radiation sources and dust populations, including gridor particle-based representations generated by hydrodynamical simulations. The dust density distribution is discretized using one of the built-in dust grids, including state-of-the art octree ), k-d tree (Saftly et al 2014), and Voronoi grids. The wide range of built-in components can be configured to construct complex models in a parameter file or through a user-friendly interface .…”