iQMC: Iterative Quasi-Monte Carlo for k-Eigenvalue Neutron Transport Simulations

TL;DR

The paper introduces iQMC, a novel iterative Quasi-Monte Carlo approach that enhances neutron transport simulations by replacing traditional quadrature methods, demonstrating improved accuracy and efficiency in k-eigenvalue problems.

Contribution

It presents the integration of iQMC into neutron transport simulations, combining it with power iteration and Davidson methods, and verifies its effectiveness on a benchmark problem.

Findings

iQMC improves solution accuracy over standard methods

Enhanced efficiency in solving k-eigenvalue problems

Validated results on Takeda-1 Benchmark problem

Abstract

The Iterative Quasi-Monte Carlo method, or iQMC, replaces standard quadrature techniques used in deterministic linear solvers with Quasi-Monte Carlo simulation for more accurate and efficient solutions to the neutron transport equation. This work explores employing iQMC in the Monte-Carlo Dynamic Code (MCDC) to solve k-eigenvalue problems for neutron transport with both the standard power iteration and the generalized Davidson method, a Krylov Subspace method. Results are verified with the 3-D, 2-group, Takeda-1 Benchmark problem.