We derive a probability distribution for the possible number of iterations required for a SIMT (single instruction multiple thread) program using rejection sampling to finish creating a sample across all threads. This distribution is found to match a recently proposed distribution from [6] that was shown as a good approximation of certain datasets. This work demonstrates an exact application of this distribution. The distribution can be used to evaluate the relative merit of some sampling methods on the GPU without resort to numerical tests. The distribution reduces to the expected geometric distribution in the single thread per warp limit. A simplified formula to approximate the expected number of iterations required to obtain rejection iteration samples is provided. With this new result, a simple, efficient layout for assigning sampling tasks to threads on a GPU is found as a function of the rejection probability without recourse to more complicated rejection sampling methods.
A myriad of nuclear reactor designs are currently being considered for next-generation power production. These designs utilize unique geometries and materials and can rely on multiphysics effects for safety and operation. This work develops a neutron transport tool, MOCkingbird, capable of three-dimensional (3D), full-core reactor simulation for previously intractable geometries. The solver is based on the method of characteristics, utilizing unstructured mesh for the geometric description. MOCkingbird is built using the MOOSE multiphysics framework, allowing for straightforward linking to other physics in the future. A description of the algorithms and implementation is given, and solutions are computed for two-dimensional/3D C5G7 and the Massachusetts Institute of Technology BEAVRS benchmark. The final result shows the application of MOCkingbird to a 3D, full-core simulation utilizing 1.4 billion elements and solved using 12 000 processors.
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