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References

The following works informed the numerical methods implemented in this package.

View factor theory

  • Howell, J. R., Mengüç, M. P., Daun, K., & Siegel, R. (2021). Thermal Radiation Heat Transfer (7th ed.). CRC Press. — View factor definitions, the reciprocity relation, and Hottel's crossed-string method for 2D geometries.

  • Howell, J. R. A Catalog of Radiation Heat Transfer Configuration Factors (3rd ed.). https://www.thermalradiation.net — Section C ("Factors from finite areas to finite areas") provides the published reference values used by the validation suite in benchmarks/howell/ (see Validation: Howell Catalog).

  • Hamilton, D. C., & Morgan, W. R. (1952). Radiant-interchange configuration factors. NACA Technical Note 2836. — A study that checks the configuration-factor solutions then in the literature, gives the more complicated ones as families of curves, and adds new cases (rectangles, triangles, finite-length cylinders).

Finite element geometry

  • Zienkiewicz, O. C., Taylor, R. L., & Zhu, J. Z. (2005). The Finite Element Method: Its Basis and Fundamentals (6th ed.). Elsevier. — Quad8 serendipity and Tri6 shape functions (Chapter 4), isoparametric mapping and Gauss quadrature on reference elements (Chapter 5).

Singularity treatment (Duffy transformation)

  • Duffy, M. G. (1982). Quadrature over a pyramid or cube of integrands with a singularity at a vertex. SIAM Journal on Numerical Analysis, 19(6), 1260–1262. — The original transformation for integrands with a singularity at a vertex of a square-based pyramid or a cube. DuffyKernel.jl implements an elementary "biggest-coordinate" generalization of it (4 regions for a common vertex, 6 for a common edge), not the specific Sauter–Schwab region formulas below.

  • Sauter, S. A., & Schwab, C. (2011). Boundary Element Methods. Springer. — Chapter 5: the Sauter–Schwab regularizing coordinate transformations for the singular panel pairs (identical or common-face, common-edge, common-vertex); a related but distinct 4D Duffy-type regularization for the same singularity, kept here as background reading rather than as the implemented method.

Gaussian quadrature

  • Golub, G. H., & Welsch, J. H. (1969). Calculation of Gauss quadrature rules. Mathematics of Computation, 23(106), 221–230. — The Golub–Welsch algorithm (nodes and weights from the eigenvalues and first eigenvector components of a symmetric tridiagonal matrix) used in Quadrature.jl to generate n-point Gauss–Legendre rules for n > 5.

  • Dunavant, D. A. (1985). High degree efficient symmetrical Gaussian quadrature rules for the triangle. International Journal for Numerical Methods in Engineering, 21(6), 1129–1148. — Dunavant triangle quadrature rules used for Tri3 and Tri6 surface elements: the degree 1, 2, 5 and 7 rules, with 1, 3, 7 and 13 points.

Ray–triangle intersection

  • Möller, T., & Trumbore, B. (1997). Fast, minimum storage ray/triangle intersection. Journal of Graphics Tools, 2(1), 21–28. — Möller–Trumbore algorithm implemented in BVH.jl (and GPUBVH.jl on the device) for obstruction testing in 3D.

BVH traversal

  • Torres, R., Martín, P. J., & Gavilanes, A. (2009). Ray casting using a roped BVH with CUDA. Proceedings of the 25th Spring Conference on Computer Graphics (SCCG '09), 95–102. ACM. — Stackless BVH traversal using a skip pointer (also called a skip connection or escape index): the node to continue with when the ray misses a node's box or the node is a leaf. GPUBVH.jl uses this encoding (its miss_link) to eliminate per-thread stack memory on GPU.

Monte Carlo integration

  • Pharr, M., Jakob, W., & Humphreys, G. (2023). Physically Based Rendering: From Theory to Implementation (4th ed.). MIT Press. — Monte Carlo integration and its variance reduction, including stratified sampling (Chapter 2, §2.2.1): background for the stratified area-sampling scheme in MCKernel.jl.

  • Cohen, M. F., & Wallace, J. R. (1993). Radiosity and Realistic Image Synthesis. Academic Press. — Form factors and the radiosity method in computer graphics: background for the cosine-weighted ray-shooting estimator in RayTraceKernel.jl and GPURayTraceKernels.jl.

  • Duff, T., Burgess, J., Christensen, P., Hery, C., Kensler, A., Liani, M., & Villemin, R. (2017). Building an orthonormal basis, revisited. Journal of Computer Graphics Techniques, 6(1), 1–8. — The branchless orthonormal-basis construction (Listing 3, using copysign) used to turn a surface normal into the frame for cosine-weighted hemisphere sampling in RayTraceKernel.jl and GPURayTraceKernels.jl.

GPU pseudo-random number generation

  • Marsaglia, G. (2003). Xorshift RNGs. Journal of Statistical Software, 8(14), 1–6. — 32-bit xorshift generator used in the sampling hot loop of GPUMCKernels.jl (and reused by GPURayTraceKernels.jl) for per-thread random streams with no heap allocation.

  • Steele, G. L., Lea, D., & Flood, C. H. (2014). Fast splittable pseudorandom number generators. ACM SIGPLAN Notices, 49(10), 453–472. — The SplitMix 64-bit mixing function (no loops or conditionals, so suitable for GPU code), used to derive independent per-thread seeds from the global seed and thread index.