Univel-based computational geometric modeling using high-dimensional material types with application to Monte Carlo nuclear particle transport
Computer graphics and geometric modeling often use unstructured surface meshes to define objects. This can result in complex, time-expensive calculations to simulate surface interactions when simulating physical processes or rendering images. This thesis describes a computational geometric model based on discrete uniform-volume elements (univels), and applies this approach to well-known problem: using the Monte Carlo method to simulate the transport physics of neutral particles (neutrons and photons) through complex geometric models. The most consequential product of this work is Juniper, a comprehensive transport modeling software system useful for both practical applications and experimental research in particle transport. Using a structured Cartesian grid of univels has several promising advantages: tracking particles through a univel grid is known to be much faster than alternative geometries. And univel-based particle tracking is particularly insensitive to the complexity of the geometric model. To use these advantages Juniper must rasterize the input model into univels. Antialiasing is a well-known technique in computer graphics to reduce the visual impact of discretization artifacts. In existing graphics applications this is almost entirely done with three-dimensional color vectors. Juniper is designed to explore antialiasing the geometry univelization, while developing novel ways to cope with high-dimensionality material vectors. Antialiasing creates blended vectors near high-frequency information areas of the rasterization grid. When the grid is an image the vectors are on a three-dimensional color space and can often be stored and interpreted directly. But for particle transport the univel values are high-dimensionality material vectors. An exact representation of their blended forms yields impractically large model sizes. Instead, these vectors can be quantized to a manageable set of prototype vectors, reducing the univel grid to a table of indices. The quantized material vectors retain the computational advantages of univelized particle transport while potentially improving the fidelity of the transport results. Exploring this problem has provided new insights into digitization of high-dimensional values, effects of univel size on transport result accuracy, and the antialiasing of high-dimensional vector spaces. A new library of carefully defined high-precision cargo object models in a universal format (XML) is another result.