A Simple Ray Acceleration Structure for Non-LTE Radiative Transfer

TL;DR

This work presents a GPU-friendly ray acceleration framework for non-LTE radiative transfer that combines variance-limited mipmapping, sparse voxel grids, and a hierarchical ray traversal (HDDA) to dramatically speed up the formal solution. It extends to dynamic atmospheres via Velocity Grids and the Core and Voigt methods, enabling anisotropic emissivity/opacity handling with controllable accuracy. The DexRT implementation demonstrates order-of-magnitude speedups while keeping the 99.9th percentile error under 0.5–1% across test cases, and highlights strong performance in realistic solar atmospheric models. The approach offers a practical path to scalable non-LTE RT, potentially adaptable to other transport problems and compatible with existing rasterization- and ray-tracing-inspired acceleration techniques. The work also discusses prefiltering and future integrations with swept methods to further enhance efficiency and accuracy.

Abstract

We present a novel ray acceleration structure for radiative transfer outside of local thermodynamic equilibrium (non-LTE), leveraging techniques from computer graphics to improve computational efficiency. By applying mipmapping (local recursive spatial averaging) and sparse voxel grids, we exploit spatial coherence and sparsity in astrophysical models to accelerate the formal solution of the radiative transfer equation. We introduce a variance-limited mipmapping (VLM) scheme with tunable error control, and extend it to handle anisotropic emission via two methods: velocity interpolation, and so-called "Core and Voigt". Our approach integrates a hierarchical digital differential analyzer (HDDA) for efficient ray traversal, which, combined with the mipmapping scheme achieves an order of magnitude speedup with less than 0.5 % error in the 99.9th percentile of the level populations. These methods are implemented in the DexRT code and demonstrate significant performance gains in realistic solar atmospheric models.

Figures (7)

• Figure 1: Illustration of the traversal problem in radiative transfer. If all voxels have non-trivial optical thickness with different emissivity and opacity (illustrated by A and B being light grey, and C and D being dark grey) then the direction of traversal through the grid has a significant impact. Whilst propagating through equivalent voxels in a different order, the opposed rays $\alpha$ and $\beta$ see very different results. Similarly, rays $\gamma$ and $\delta$ which have the same direction but different origins see quite different results, due to only traversing a subset of the domain. A worked example is shown in Table \ref{['Tab:WorkedExample']}.
• Figure 2: A demonstration of the process of successive spatial averaging in mipmapping applied to the opacity $\chi$ in the hydrogen Ly$\,\alpha$ line core in a model. For each subsequent MIP level, the effective resolution is reduced by a factor of 2 on each spatial axis by applying a 2x2 box filter. Due to the decreasing size of the image with successive MIPs this set of images is known as a MIP pyramid or MIP chain.
• Figure 3: Values of the absolute value of the index of dispersion (IoD -- variance of the voxels in the filter divided by the mean) for each MIP level of $\ln{\left( \chi \Delta s \right)}{}$ given the opacity distribution in Figure \ref{['Fig:Mips']}. The higher this metric, the higher the variance in a pixel, and thus the more error will likely result from mipping this region to this level.
• Figure 4: The result of applying our adaptive mipmapping technique independently to three wavelengths of opacity of our model shown in Figure \ref{['Fig:Mips']}. Each wavelength uses an IoD threshold of 1, and will not average further if a block reaches this threshold. From left to right we show each individually mipped wavelength, the MIP level of each block, and the overlap of these mipmapped opacities (mapped into the red, green, and blue channels and scaled for visibility). The set of MIP levels shows that fine structure is present in different locations in the different wavelengths. The fractions of voxels in each MIP level at each wavelength is shown in Table. \ref{['Tab:MipFractions']}
• Figure 5: An example of our adaptive grid scheme and hierarchical digital differential analyser (HDDA) scheme, for a discretised model with with a full resolution of $32\times32$ (indicated in grey). The adaptive grid traced by the ray is determined as described in Section \ref{['Sec:Vlm']}. Several ray intersection types are shown: with the model bounding box as red triangles, internally to the model as red circles, and on resolution change with blue crosses.