General order nodal transport methods and application to parallel computing

Highly accurate solutions for neutron transport problems are achievable using high order nodal methods, such as the General Order Nodal Transport (GONT) class of methods. The final equations for these methods constitute a set of Weighted Diamond-Difference (WDD) equations that are solved using standard mesh sweeps. A parallel algorithm for solving these equations, based on decomposition of the angular domain is particularly suited for message-passing computers as it embodies a statically-scheduled, coarse-grained parallelization. The parallel code, P-GONT implemented on Intel's iPSC/2 hypercube produces large speedup factors at very high parallel efficiencies. A mathematical model for execution time as a function of the problem parameters: spatial approximation order, number of mesh cells, and angular quadrature order, as well as the number of utilized processors, agrees very well with measured results. The model shows that the parallel efficiency is insensitive to the number of mesh cells, but improves with the spatial approximation and angular quadrature orders. It also shows that the speedup factor increases monotonically with the number of utilized processors, if the latter divides exactly the number of independent processes. 35 refs.,.5 figs., 1 tabs