An Energy-Group and Angular-Direction Parallel Method for Steady-State Multigroup Neutron Transport Using Least-Squares Finite Elements

摘要: An energy-group/angular-direction block Jacobi parallel method based on source lagging is developed for steady-state multigroup discrete ordinates (S_N) transport discretized using the least-squares finite element method (LSFEM). Each parallel task solves the complete spatial linear system for one energy group and one angular direction. At the beginning of each iteration, the scattering source, fission source, and incident flux at reflective boundaries are constructed from the previous angular flux and held fixed throughout the solution stage, allowing the fixed-source subproblems to be solved concurrently. Centralized source evaluation, reuse of discrete operators, and an improved initial-guess strategy for the inner solver further reduce computational cost. Three two-dimensional, two-group benchmarks, C4V, BWR, and an LWR assembly with burnable absorbers, are used to compare the results and performance of the original serial implementation and the source-lagging formulation. The relative L² differences in the two-group fluxes do not exceed 0.0332% for any benchmark. With four workers, the end-to-end runtimes are reduced to 1/2.32, 1/7.26, and 1/2.36 of the original serial runtimes, respectively. Source lagging increases the number of outer iterations by factors of 1.81–2.24; the lower cost per iteration yields an overall runtime reduction in all three cases. The one-worker control shows that parallel execution accelerates BWR and LWR but slows C4V, illustrating how task granularity and execution overhead affect the benefit of group–direction parallelism.