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In this work we investigate replacing standard quadrature techniques used indeterministic linear solvers with a fixed-seed Quasi-Monte Carlo calculation toobtain more accurate and efficient solutions to the neutron transport equation(NTE). Quasi-Monte Carlo (QMC) is the use of low-discrepancy sequences tosample the phase space in place of pseudo-random number generators used bytraditional Monte Carlo (MC). QMC techniques decrease the variance in thestochastic transport sweep and therefore increase the accuracy of the iterativemethod. Historically, QMC has largely been ignored by the particle transportcommunity because it breaks the Markovian assumption needed to model scatteringin analog MC particle simulations. However, by using iterative methods the NTEcan be modeled as a pure-absorption problem. This removes the need toexplicitly model particle scattering and provides an application well-suitedfor QMC. To obtain solutions we experimented with three separate iterativesolvers: the standard Source Iteration (SI) and two linear Krylov Solvers,GMRES and BiCGSTAB. The resulting hybrid iterative-QMC (iQMC) solver wasassessed on three one-dimensional slab geometry problems. In each sampleproblem the Krylov Solvers achieve convergence with far fewer iterations (up to8x) than the Source Iteration. Regardless of the linear solver used, the hybridmethod achieved an approximate convergence rate of $O(N^{-1})$, as compared tothe expected $O(N^{-1/2})$ of traditional MC simulation, across all testproblems.

A Quasi-Monte Carlo Method with Krylov Linear Solvers for Multigroup Neutron Transport Simulations