This talk presents an extension of the traditional slice balance approach (SBA) that is more accurate and allows for two new methods of parallelization of discrete ordinates transport sweeps. The accuracy of the new approach is compared to the traditional cell balance and slice balance methods for both the diamond difference (DD) and linear discontinuous finite element (LDFE) spatial discretization schemes. The results show that the alterations made to the traditional SBA reduce numerical diffusion of the solution in the vicinity of discontinuities for both DD and LDFE. Manufactured solutions are used to analyze the convergence rate of the traditional cell balance and slice balance approaches and the extended SBA for both smooth and discontinuous solutions. The new methods of parallelization reduce or eliminate processor idle time and one of these methods allows for an arbitrary domain decomposition scheme with no restriction on the smoothness of the inter-node domain boundaries. A weak scaling study is performed to characterize the parallel efficiency of the proposed methods. Furthermore, through the use of graphics processing units (GPUs) the time required to compute geometric quantities on a per-slice basis, which cannot be precomputed and stored due to excessive memory requirements, can be significantly reduced and perhaps even hidden altogether by pipelining the geometric setup and transport sweep routines on the GPU and CPU respectively.
