Performance and performance modeling of a parallel algorithm for solving the neutron transport equation

Abstract

A parallel algorithm is derived for solving the discrete-ordinates approximation of the neutron transport equation, based on the naturally occurring decoupling between the mesh sweeps in the various discrete directions during each iteration. In addition, the parallel Source Iteration (SI) algorithm, characterized by its coarse granularity and static scheduling, is implemented for the Nodal Integral Method (NIM) into the Parallel Nodal Transport (P-NT) code on Intel's iPSC/2 hypercube. Measured parallel performance for solutions of two test problems is used as evidence of the parallel algorithm's potential for high speedup and efficiency. The measured performance data are also used to develop and validate a parallel performance model for the total, serial, parallel, and global-summation time components per iteration as a function of the spatial mesh size, the problem size (number of mesh cells and angular quadrature order), and the number of utilized processors. The potential for high performance (large speedup at high efficiency) for large problems is explored using the performance model, and it is concluded that present applications in three-dimensional Cartesian geometry will benefit by concurrent execution on parallel computers with up to a few hundred processors.