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A crucial ingredient for numerically solving the 3D radiative transferproblem is the choice of the grid that discretizes the transfer medium. Manymodern radiative transfer codes, whether using Monte Carlo or ray tracingtechniques, are equipped with hierarchical octree-based grids to accommodate awide dynamic range in densities. We critically investigate two differentaspects of octree grids in the framework of Monte Carlo dust radiativetransfer. Inspired by their common use in computer graphics applications, wetest hierarchical k-d tree grids as an alternative for octree grids. On theother hand, we investigate which node subdivision-stopping criteria are optimalfor constructing of hierarchical grids. We implemented a k-d tree grid in the3D radiative transfer code SKIRT and compared it with the previouslyimplemented octree grid. We also considered three different nodesubdivision-stopping criteria (based on mass, optical depth, and densitygradient thresholds). Based on a small suite of test models, we compared theefficiency and accuracy of the different grids, according to various qualitymetrics. For a given set of requirements, the k-d tree grids only require halfthe number of cells of the corresponding octree. Moreover, for the same numberof grid cells, the k-d tree is characterized by higher discretization accuracy.Concerning the subdivision stopping criteria, we find that an optical depthcriterion 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 approximaterecipe, this can lead to a 20% reduction in the number of cells needed to reacha certain grid quality. An additional density gradient threshold criterion canbe added that solves the problem of poorly resolving sharp edges and...(abridged).

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