Neutron transport, diffusion, and diffusion synthetic acceleration methods for parallel architecture computers.

The main goal of this work is to examine efficient methods for solving neutron transport and diffusion problems on parallel architecture computers. Using geometric domain decomposition methods, we describe a modified (parallel) version of the standard (scalar) Source Iteration (SI) scheme to solve the diamond-differenced discrete ordinates (S$\sb{\rm N}$) equations for one-group, isotropic scattering and isotropic source transport problems. This parallel SI method consists of subdividing the spatial subdomain for the problem and performing the transport sweeps independently on each subdomain (processor). Results of test runs for one-dimensional transport problems on the Ncube/six, a distributed memory message passing computer, and for x,y-geometry problems on the IBM RP3, a shared memory computer, indicate that this strategy works efficiently provided the subdomains are optically thick or contain many cells. Next, we develop a multigrid method to efficiently solve heterogeneous diffusion problems. A Fourier analysis technique is presented to explicitly measure the performance of the conventional and new methods. The results of the Fourier analysis show that the convergence rate of our multigrid method is faster than that of conventional methods in slab and x,y-geometry diffusion problems. We also present an implementation of our multigrid method on the RP3 computer for x,y-geometry diffusion problems. The performance of the new multigrid method degrades with an increasing number of processors, not because of the degradation in the convergence rate, but because of the domination of communication overhead and unemployment of some processors on the coarse grids. Finally, we describe a parallel Diffusion Synthetic Acceleration (DSA) method for the rapid solution of S$\sb{\rm N}$ problems. The DSA algorithm is a combination of a parallel SI algorithm for the transport operator and a parallel multigrid algorithm for the diffusion operator. This diffusion operator has a one-point removal term with linear consistency terms. Thus, multigrid methods can be used to solve it efficiently. We describe the implementation of the DSA algorithm for the IBM RP3 computer in x,y-geometry. The performance of the DSA algorithm degrades with an increasing number of processors. However, as is commonly the case with parallel methods, this degradation is not important provided that the amount of work assigned to each processor is large compared to the communication overhead between processors.PhDNuclear EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105632/1/9135726.pdfDescription of 9135726.pdf : Restricted to UM users only