A Hybrid Deterministic/Monte Carlo Method for Solving the k-Eigenvalue Problem with a Comparison to Analog Monte Carlo Solutions

In this article we present a hybrid deterministic/Monte Carlo algorithm for computing the dominant eigenvalue/eigenvector pair for the neutron transport k-eigenvalue problem in multiple space dimensions. We begin by deriving the Nonlinear Diffusion Acceleration method (Knoll, Park, and Newman, 2011; Park, Knoll, and Newman, 2012) for the k-eigenvalue problem. We demonstrate that we can adapt the algorithm to utilize a Monte Carlo simulation in place of a deterministic transport sweep. We then show that the new hybrid method can be used to solve a two-group, two dimensional eigenvalue problem. The hybrid method is competitive with analog Monte Carlo in terms of number of particle flights required to compute the eigenvalue; however it produces a much less noisy eigenvector and fission source distribution. Furthermore, we show that we can reduce the error induced by the discretization of the low-order system by appropriate refinement of the mesh.