Parallelization of 1-D Transport Sweeps

Peter Maginot, Texas A&M University

Accurate modeling of a wide range of scientific phenomena and engineering problems, such as supernova explosions, nuclear fusion, high energy density physics experiments and nuclear power reactors, requires the solution of time-dependent radiation transport problems. Due to the large number of unknowns (space x frequency x angle), high-resolution time-dependent radiation transport problems are only feasible with parallel computing. However, the advection term in discontinuous finite element (DFEM) radiation transport calculations creates an inherently serial dependence between spatial cells. That is, in the direction of radiation flow, while “sweeping” through the spatial mesh, the solution within each cell can only be found after the solution in every previous, or upwind, cell has been found. While this has no effect when computing in serial, this obviously cannot scale in parallel computing environments. In multiple spatial dimensions, the Koch-Baker-Alcouffe algorithm, though not perfect, minimizes the pipe-fill/pipe-empty time penalty to an acceptable level. However, there is no spatial analog to 1-D spatial geometry. Building on earlier work, we show that by casting 1-D transport sweeps as the canonical partial sum problem of parallel computing, they can be parallelized with only a modest penalty. We provide the results from initial scaling and speed-up studies demonstrating the concept and viability of parallel 1-D transport sweeps for linear DFEM and show that issues with using higher order DFEM can be ameliorated with the correct choice in numerical quadrature.

Abstract Author(s): Peter Maginot, Jim Morel, Jean Ragusa