@article{hu_smith_willert_kelley_2014, title={High-Dimensional Model Representations for the Neutron Transport Equation}, volume={177}, ISSN={["1943-748X"]}, DOI={10.13182/nse13-52}, abstractNote={Abstract The Boltzmann transport equation is used to model the neutron flux in a nuclear reactor. The solution of the transport equation is the neutron flux, which depends on a large number of material cross sections that can be on the order of thousands. These cross sections describe various types of possible interactions between neutrons, such as fission, capture, and scattering. The cross sections are measured experimentally and therefore have associated uncertainties. It is thus necessary to quantify how the uncertainty of the cross-section values is propagated through the model for the neutron flux. High-dimensional model representations (HDMRs) can be employed to systematically quantify input-output relations. It can, however, be computationally prohibitive to construct a surrogate model using the HDMR framework for a model that has thousands of parameters. In this paper, we introduce an algorithm that utilizes the New Morris Method to first reduce the parameter space to include only the significant individual and pairwise effects and then construct a surrogate model using a Cut-HDMR expansion within the reduced space. A unified index is introduced to facilitate the comparison of the significance of the model parameters. The accuracy and efficiency of the surrogate model is demonstrated using a one-dimensional neutron transport equation.}, number={3}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Hu, Zhengzheng and Smith, Ralph C. and Willert, Jeffrey and Kelley, C. T.}, year={2014}, month={Jul}, pages={350–360} }
 @article{willert_kelley_knoll_park_2013, title={HYBRID DETERMINISTIC/MONTE CARLO NEUTRONICS}, volume={35}, ISSN={["1095-7197"]}, DOI={10.1137/120880021}, abstractNote={In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing high-order problem and a Jacobian-free Newton--Krylov iteration for the low-order problem. We couple the Monte Carlo solution with the low-order problem using filtering to smooth the flux and current from the Monte Carlo solver and an analytic Jacobian-vector product to avoid numerical differentiation of the Monte Carlo results. We use a continuous energy deposition tally for the Monte Carlo simulation. We conclude the paper with numerical results which illustrate the effectiveness of the new algorithm.}, number={5}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Willert, Jeffrey and Kelley, C. T. and Knoll, D. A. and Park, H.}, year={2013}, pages={S62–S83} }
 @article{willert_kelley_knoll_park_2013, title={Scalable Hybrid Deterministic/Monte Carlo Neutronics Simulations in Two Space Dimensions}, DOI={10.1109/dcabes.2013.8}, abstractNote={In this paper we discuss a parallel hybrid deterministic/Monte Carlo (MC) method for the solution of the neutron transport equation in two space dimensions. The algorithm uses an NDA formulation of the transport equation, with a MC solver for the high-order equation. The scalability arises from the concentration of work in the MC phase of the algorithm, while the overall run-time is a consequence of the deterministic phase.}, journal={2013 12TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING AND APPLICATIONS TO BUSINESS, ENGINEERING & SCIENCE (DCABES)}, author={Willert, Jeffrey and Kelley, C. T. and Knoll, D. A. and Park, H.}, year={2013}, pages={7–10} }
 @article{willert_kelley_knoll_dong_ravishankar_sathre_sullivan_taitano_2012, title={Hybrid Deterministic/Monte Carlo Neutronics using GPU Accelerators}, DOI={10.1109/dcabes.2012.37}, abstractNote={In this paper we discuss a GPU implementation of a hybrid deterministic/Monte Carlo method for the solution of the neutron transport equation. The key feature is using GPUs to perform a Monte Carlo transport sweep as part of the evaluation of the nonlinear residual and Jacobian-vector product. We describe the algorithm and present some preliminary numerical results which illustrate the effectiveness of the GPU Monte Carlo sweeps.}, journal={2012 11TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING AND APPLICATIONS TO BUSINESS, ENGINEERING & SCIENCE (DCABES)}, author={Willert, Jeff and Kelley, C. T. and Knoll, D. A. and Dong, Han and Ravishankar, Mahesh and Sathre, Paul and Sullivan, Michael and Taitano, William}, year={2012}, pages={43–47} }