Transport Sweeps Using an Improved Slice Balance Approach With LDFE and GPU Acceleration

Richard Vega, Texas A&M University

This research presents an improvement to the traditional Slice Balance Approach (SBA) that is more accurate and allows for a new method 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. A manufactured solution is used to confirm that the second-order convergence rate of the LDFE spatial discretization scheme is retained for a smooth solution when the improved SBA is applied. The new method of parallelization exhibits no processor idle time and allows for an arbitrary domain decomposition scheme, with no restriction on the smoothness of the inter-node domain boundaries. These advantages are gained at the cost of higher communication and memory demand. The added communication is coalesced into a small number of messages and the added memory requirement is that the entire mesh (not the entire solution) be duplicated on each node. This added memory requirement is roughly 320 bytes per spatial cell in the mesh. A weak scaling study is performed to characterize the parallel efficiency of the proposed method. Furthermore, through the use of graphics processing units (GPUs), the time required to compute geometric quantities on a per-slice basis, which cannot be pre-computed and stored due to excessive memory requirements, can be significantly reduced and perhaps even hidden altogether by pipe-lining the geometric setup and transport sweep routines on the GPU and CPU respectively.

Abstract Author(s): Richard M. Vega