Parallelization of a spherical S(sub N) algorithm based on the spatial domain decomposition.

摘要

The SN method is an approximate approach used to solve the linear Boltzmann transport theory equation. This method requires a significant amount of memory and computational time which are limiting factors for its utility in real-life applications. In the past decade, the significant advancements in computer hardware design (vector and parallel processing) have provided the possibility of development of new parallel/vector software which can operate significantly faster than the older serial/scalar ones. In, recent years, several studies have been performed on the vector/parallel processing of the SN transport theory method. This paper primarily discusses a parallel algorithm for the S. method which is based on decomposition of the spatial domain. Wienke and coworkers have performed studies on the energy domain and have obtained significant speedups. Azmy considered angular parallelization of a one-group x-y nodal SN algorithm and recently Rhoades and Flanery performed angular parallelization for a x-y-z SN transport formulation. Haghighat and Mattis considered angular parallelization of a curvilinear SN algorithm. For parallelization based on the spatial domain decomposition only one study has been reported by Yavuz and Larsen who demonstrated the possibility of spatial decomposition for a slab geometry on a sedal machine. In the present work, we develop a spatial parallel formulation for spherical geometry and study its behavior under different physical conditions. Then, we describe our implementation of the algorithm on the Cornell National Supercomputer Facility IBM 3990/600J with six processors and measure speedups for different problem sizes.