Creating and Using a Type of Free-Form Geometry in Monte Carlo Particle Transport

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Abstract
While the reactor physicists were fine-tuning the Monte Carlo paradigm for particle transport in regular geometries, the computer scientists were developing rendering algorithms to display extremely realistic renditions of irregular objects ranging from the ubiquitous teakettle to dynamic Jell-O. For many years, the modeling commonality of these apparently diverse disciplines was either largely ignored or unnoticed by many members in both technical communities. Apparently, with the exception of a few visionaries such as the Mathematical Application Group, Inc. (MAGI), each community was not sufficiently aware of what the other was doing. This common basis included the treatment of neutral particle transport through complicated geometries in three-dimensional space. In one instance, it is called the Boltzmann transport equation, while in the other, it is commonly referred to as the rendering equation. Even though the modeling methods share a common basis, the initial strategies each discipline developed for variance reduction were remarkably different. Initially, the reactor physicist used Russian roulette, importance sampling, particle splitting, and rejection techniques. In the early stages of development, the computer scientist relied primarily on rejection techniques, including a very elegant hierarchical construction and sampling method. This sampling method allowed the computer scientist to viably track particles through irregular geometries in three-dimensional space, while the initial methods developed by the reactor physicists would only allow for efficient searches through analytical surfaces or objects. As time goes by, it appears there has been some merging of the variance reduction strategies between the two disciplines. This is an early (possibly first) incorporation of geometric hierarchical construction and sampling into the reactor physicists’ Monte Carlo transport model that permits efficient tracking through nonuniform rational B-spline surfaces in three-dimensional space. After some discussion, the results from this model are compared with experiments and the model employing implicit (analytical) geometric representation.

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