A Hybrid Parallel Algorithm for the 3-D Method of Characteristics Solution of the Boltzmann Transport Equation on High Performance Compute Clusters.

Abstract

The focus of this thesis is on the development of a highly scalable parallel algorithm for solving the 3-D method of characteristics (MOC) form of the Boltzmann neutron transport equation. The derivation of the 3-D MOC method is presented first, along with the details of the discretization techniques, that utilize the concept of modular ray tracing. The implementation of these equations is then described, and then the approach to parallelizing the algorithm is discussed. Results are shown for a range of benchmark problems typically solved by 3-D neutron transport codes. The algorithm is parallelized in space, angle, and by characteristic rays, which is specific to the MOC solution method. Once the parallel algorithm is established, a performance model for the particular implementation is derived. This model contains detailed expressions for the number of floating point operations and execution time as a function of the problem size and fundamental computer hardware properties, such as the time per flop and cache access latency. The procedure for determining the hardware coefficients required by the performance model is then presented and validated using experimental results. The performance model is shown to agree well with experiment for both types of execution, and the model is therefore used for subsequent analyses that explore the algorithm's sensitivities to the computer and network hardware characteristics. The model is also analyzed to assess the scaling of the algorithm for a quarter core PWR. The optimization of the convergence of the parallel 3-D MOC algorithm through the use of the coarse mesh finite difference (CMFD) method is then developed. The CMFD accelerated parallel 3-D MOC algorithm is then used to compute solutions to several numerical benchmarks, that show good agreement with the reference results. Finally, the research performed in this thesis and its conclusions are summarized, and areas of future research are suggested.