Iterative Methods for Solvingx-yGeometrySNProblems on Parallel Architecture Computers

Abstract

In this paper, geometric domain decomposition methods are described for solving x-y geometry discrete ordinates (S[sub N]) problems on parallel architecture computers. First, a parallel source iteration scheme is developed; here, one subdivides the spatial domain of the problem, performs transport sweeps independently in each subdomain, and iterates on the scattering source and the interface fluxes between each subdomain. Second, a parallel diffusion synthetic acceleration (DSA) scheme is developed to speed up the convergence of the parallel source iteration. These schemes have been implemented on the IBM RP3, a shared/distributed memory parallel computer. The numerical results show that the parallel source iteration and DSA methods both exhibit significant speedups over their scalar counterparts, but that a degradation in parallel efficiency occurs due to the geometric domain decomposition (iteration on interface fluxes) and the overhead time required for the communication of data between processors.