Tetrahedral grids in Monte Carlo radiative transfer

Abstract: Context. 3D numerical simulations of radiative transfer are crucial for understanding complex astrophysical objects. For Monte Carlo radiative transfer, the spatial grid design is critical yet complex. Common grids include hierarchical octree and unstructured Voronoi grids, each with its own strengths and weaknesses. Tetrahedral grids, widely used in ray-tracing graphics, are a potential alternative. Aims. We explore the possibilities, advantages, and limitations of tetrahedral grids for Monte Carlo radiative transfer, comparing their performance with other grid structures. Method. We integrated a tetrahedral grid structure, using the TetGen library, into the SKIRT Monte Carlo radiative transfer code. Tetrahedral grids can be imported or adaptively constructed and refined within SKIRT. We implemented an efficient grid traversal method using Pl\"ucker coordinates and Pl\"ucker products. Results. We validated the tetrahedral grid construction and traversal algorithm with 2D radiative transfer benchmarks. In a simple 3D model, we compared the performance of tetrahedral, octree, and Voronoi grids. The octree grid outperformed the others in traversal speed, while the tetrahedral grid had the lowest grid quality. Overall, tetrahedral grids performed worse than octree and Voronoi grids. Conclusion. While tetrahedral grids may not be ideal for most astrophysical simulations, they offer a viable unstructured alternative to Voronoi grids for specific applications, such as post-processing hydrodynamical simulations on tetrahedral or unstructured grids.