Parallel algorithms for nuclear reactor analysis via domain decomposition method

Abstract

In this thesis, the neutron diffusion equation in reactor physics is discretized by the finite difference method and is solved on a parallel computer network which is composed of T-800 transputers. T-800 transputer is a message-passing type MIMD (multiple instruction streams and multiple data streams) architecture. A parallel variant of Schwarz alternating procedure for overlapping subdomains is developed with domain decomposition. The thesis provides convergence analysis and improvement of the convergence of the algorithm. The convergence of the parallel Schwarz algorithms with DN(or ND), DD, NN, and mixed pseudo-boundary conditions(a weighted combination of Dirichlet and Neumann conditions) is analyzed for both continuous and discrete models in two-subdomain case and various underlying features are explored. The analysis shows that the convergence rate of the algorithm highly depends on the pseudo-boundary conditions and the theoretically best one is the mixed boundary conditions(MM conditions). Also it is shown that there may exist a significant discrepancy between continuous model analysis and discrete model analysis. In order to accelerate the convergence of the parallel Schwarz algorithm, relaxation in pseudo-boundary conditions is introduced and the convergence analysis of the algorithm for two-subdomain case is carried out. The analysis shows that under-relaxation of the pseudo-boundary conditions accelerates the convergence of the parallel Schwarz algorithm if the convergence rate without relaxation is negative, and any relaxation(under or over) decelerates convergence if the convergence rate without relaxation is positive. Numerical implementation of the parallel Schwarz algorithm on an MIMD system requires multi-level iterations: two levels for fixed source problems, three levels for eigenvalue problems. Performance of the algorithm turns out to be very sensitive to the iteration strategy. In general, multi-level iterations provide good performance w...