A Multiple-Set Overlapping-Domain Decomposed Monte Carlo Synthetic Acceleration Method for Linear Systems

¹ University of Wisconsin - Madison, Engineering Physics Department, 1500 Engineering Dr., Madison, WI 53706
² Oak Ridge National Laboratory, Reactor and Nuclear Systems Division, 1 Bethel Valley Rd., Oak Ridge, TN 37831

Abstract

We present a multiple-set overlapping-domain decomposed strategy for parallelizing the Monte Carlo Synthetic Acceleration method. Monte Carlo Synthetic Acceleration methods use the Neumann-Ulam class of Monte Carlo solvers for linear systems to accelerate a fixed-point iteration sequence. Effective parallel algorithms for these methods require the parallelization of the underlying Neumann-Ulam solvers. To do this in a domain decomposed environment, we borrow strategies traditionally implemented in Monte Carlo particle transport to parallelize the problem. The parallel Neumann-Ulam and multiple-set overlapping-domain decomposition algorithms are presented along with parallel scaling data for the resulting implementation using the Titan Cray XK7 machine at Oak Ridge National Laboratory.