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Burke, Timothy P.

Publications and source records attributed to Burke, Timothy P..

11 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Monte Carlo estimates of sensitivities to geometric perturbations for shielding problems using kernel density estimators - 25605

A Monte Carlo method to estimate the sensitivity of reaction rates like dose and flux spectra to geometric perturbations using kernel density estimators is demonstrated for shielding problems. The method is used to estimate the sensitivity of the spectrum emitted from a Cf-252 source at the center of an iron sphere as well as the sensitivity of the dose due to Cf-252 neutrons shielded using various materials. Results are compared against reference solutions obtained using Monte Carlo direct perturbations with central differences, with agreement within 5% and 3σ for the majority of results. The results indicate that a bandwidth that is 10-20% of the shielding thickness produces accurate results with statistically insignificant bias for the chosen test problems. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

The state of Monte Carlo neutron transport on GPU accelerators - A review - 25609

A review of the current state of Monte Carlo neutron transport of Graphical Processing Units (GPUs) has been performed. Up-to-date data has been solicited from researchers in the field and combined with data available in literature to provide the current state of Monte Carlo neutron transport on GPU hardware. Nine implementations of neutron transport on GPUs have been summarized and the performance results have been presented to allow the reader to compare performance. A comparison of the results has shown that researchers obtained similar performance when scaled to the performance of NVIDIA Tesla K40 GPUs. A strong scaling equation will be presented that can be used to describe the GPU performance against different numbers of CPU cores. One implementation of a production Monte Carlo code on GPU hardware, the code Shift, showed that newer NVIDIA Pascal and Volta based GPUs provide a significant performance improvement. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2017

Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

Here, Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivities of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and 3σ of reference solutions obtained using direct perturbations with central differences for the majority of test problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Kernel Density Estimation of Reaction Rates in Neutron Transport Simulations of Nuclear Reactors

Kernel density estimators (KDEs) are applied to estimate neutron scalar flux and reaction rate densities in Monte Carlo neutron transport simulations of heterogeneous nuclear reactors in continuous energy. The mean free path (MFP) KDE is introduced in order to handle the issues that arise from estimating the discontinuous reaction rate densities at material interfaces. Results show the MFP KDE is more accurate at estimating reaction rates compared with previous KDE formulations. An approximate MFP (aMFP) KDE is introduced to circumvent several practical issues presented by the MFP KDE. A volume-averaged KDE is derived and used to determine the bias introduced by the aMFP KDE. A KDE is formulated for cylindrical coordinates to better represent the geometry and capture the physics in two-dimensional reactor physics problems. The results here indicate that the cylindrical MFP KDE and cylindrical aMFP KDE are accurate tools for capturing reaction rates in heterogeneous reactor physics problems in continuous energy, with local biases of less than 1%.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Spherical Kernel Density Estimators For Monte Carlo Radiation Transport Problems

Recently, there has been interest in creating alternatives to histograms (mesh tallies) for estimating spatially-distributed quantities such as scalar flux and reaction rate densities. Kernel Density Estimators (KDEs) are non-parametric estimators that obtain estimates of the underlying distribution at user-defined points without having to specify an underlying mesh, and the uncertainty at those points is independent of the number of tally points used in the simulation. This has led to the investigation of KDEs as an attractive potential alternative to histogram tallies in Monte Carlo radiation transport simulations for reactor physics problems and shielding applications. A KDE was recently created specifically for cylindrical geometries that is capable of producing smooth and accurate estimates of flux and reaction rate densities in reactor physics problems. This work extends the cylindrical KDE and cylindrical Mean Free Path (MFP) KDE to spherical geometries and verifies the spherical KDE on bare and reflected critical benchmark problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Monte Carlo Estimates of Eigenvalue Sensitivity to System Dimensions using Kernel Density Estimators

In the last decade there has been an increasing interest in calculating sensitivity coefficients in order to quantify the impact of uncertainty in material properties and system parameters on quantities of interest. Extensive work has been done developing Monte Carlo methods to estimate eigenvalue sensitivity to material properties. While deterministic methods exist for determining the eigenvalue sensitivity to system dimensions, the use of Monte Carlo methods to efficiently calculate eigenvalue sensitivity coefficients to system dimensions is still an open topic. Current Monte Carlo methods for calculating eigenvalue sensitivity coefficients to system dimensions are inefficient. Direct Monte Carlo perturbations require two additional simulations of high statistical precision in order to determine the eigenvalue sensitivity to the location of a single boundary. If the sensitivity to the location of multiple surfaces are desired, two additional simulations must be run for each surface. Kiedrowski and Favorite extended continuous energy Monte Carlo methods for sensitivities of nuclear cross sections to calculate sensitivities to interface boundaries or system dimensions to create the only current alternative to direct Monte Carlo calculations. However this method relies on the simulation of additional random walks launched at each surface crossing event. The present method extends upon Kiedrowski's work and eliminates the inefficient portions of the calculation through the use of Kernel Density Estimators (KDEs). The new method efficiently estimates eigenvalue sensitivities to the uniform expansion or contraction of material interface boundaries or system dimensions, negligibly impacting the runtime performance of the Monte Carlo code. The new estimator is tested on bare and reflected critical configurations in spherical geometry and is compared to estimates obtained from direct Monte Carlo perturbations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

GPU Acceleration of Kernel Density Estimators in Monte Carlo Neutron Transport Simulations

Kernel Density Estimators (KDEs) have recently been explored for use in Monte Carlo radiation transport simulations as an alternative to histogram tallies for capturing spatially-resolved quantities such as neutron flux and reaction rates. Histogram tallies suffer from large uncertainties when detailed spatial resolution of the quantity of interest is required; increasing the resolution of the underlying mesh increases the uncertainty in each histogram bin. KDEs obtain estimates of underlying densities on user-defined points, with the uncertainty at those points being independent of the spatial resolution desired since collisions and particle-track segments are allowed to contribute to the score at multiple tally points. Thus, KDEs show potential for obtaining estimates of a smoother spatially-resolved with reduced variance when compared to a histogram. However, this ability that enables KDEs to obtain lower uncertainties per particle history is more computationally expensive than using a traditional histogram bins on a structured mesh. While KDEs are capable of producing lower tally uncertainties compared to histogram binning for a given number of histories, their increased computational cost may make them less efficient. Even so, it is possible to reduce this additional cost by exporting the KDE tally routines onto Graphics Processing Units (GPUs). GPUs are commonly found on high-performance computing machines as a means of increasing performance without adding additional compute nodes. While it is difficult for existing Monte Carlo radiation transport codes to take advantage of GPUs without rewriting large portions of the code, it is possible to leverage GPUs through heterogeneous computing. This work uses a modified version of OpenMC and exports the KDE tally routines onto a GPU to obtain problem-dependent speedups ranging between 1.6 and 5.0 for the problem studied in this paper. While this methodology is applied to KDEs, the same ideas can be applied to other computationally expensive vectorizable portions of Monte Carlo algorithms. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Cylindrical Kernel Density Estimators For Monte Carlo Neutron Transport Reactor Physics Problems

Kernel Density Estimators (KDEs) have been investigated as an alternative to histogram tallies in Monte Carlo radiation transport simulations for capturing spatially-resolved quantities such as scalar flux and reaction rate densities. KDEs are non-parametric estimators that show potential for producing smooth estimates of quantities of interest with reduced variance compared to traditional histogram tallies. Furthermore, KDEs obtain estimates of the underlying distribution at user-defined points without requiring an underlying mesh, thus making KDEs an attractive potential alternative to histogram tallies. Recent work has introduced the Mean Free Path based KDE (MFP KDE) in order to capture distributions with large curvature at material interfaces, e.g. absorption reaction rates in UO{sub 2} fuel in light water reactors. However, the multivariate MFP KDE produces inaccuracies in the form of localized spikes in problems with material cross sections that contain large resonances. Since the MFP KDE works well in one dimension, it is hypothesized that a different MFP KDE formulation where the normalization coefficient only contains one factor of the cross section would be able to capture these distributions with large curvature without producing spikes in the estimate. This can be accomplished by using a cylindrical KDE whose 2-D support area is wedge-shaped and applying the MFP KDE to the radial component of the cylindrical KDE. These cylindrical KDEs use 2-D (r,θ) cylindrical coordinates with no dependence in axial dimension z. This paper derives the cylindrical KDE and the cylindrical MFP KDE and tests them on a reactor physics pin-cell benchmark problem, producing accurate estimates of flux and reaction rate densities with differences less than 0.5% when compared to a reference histogram. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Flux and Reaction Rate Kernel Density Estimators in OpenMC

Current methods for obtaining flux and reaction rate profiles in a Monte Carlo simulation rely on histogram tallies that can suffer from large uncertainties when fine detail is required. Recently, another density estimation technique has been applied to Monte Carlo radiation transport sim ulations: the Kernel Density Estimator (KDE) [Banerjee, K.]. KDEs are capable of calculating the flux at a point without the necessity of tracking particles on a spatial mesh, making KDEs ideal tools for multi-physics problems. Furthermore, KDEs allow for one collision or track length to contribute to the estimate of the flux at multiple points, circumventing the large statistical uncertainties associated with fine-mesh histogram tallies. However, KDEs have only been proven to be capable of estimating flux values at a series of points; no work has been done to estimate reaction rates or other quantities of interest. Furthermore, little work has been done in optimizing the KDE bandwidth for the energy-dependence of neutron transport simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Verification of Unstructured Mesh Capabilities in MCNP6 for Reactor Physics Problems

New unstructured mesh capabilities in MCNP6 (developmental version during summer 2012) show potential for conducting multi-physics analyses by coupling MCNP to a finite element solver such as Abaqus/CAE. Before these new capabilities can be utilized, the ability of MCNP to accurately estimate eigenvalues and pin powers using an unstructured mesh must first be verified. Previous work to verify the unstructured mesh capabilities in MCNP was accomplished using the Godiva sphere, and this work attempts to build on that. To accomplish this, a criticality benchmark and a fuel assembly benchmark were used for calculations in MCNP using both the Constructive Solid Geometry (CSG) native to MCNP and the unstructured mesh geometry generated using Abaqus/CAE. The Big Ten criticality benchmark was modeled due to its geometry being similar to that of a reactor fuel pin. The C5G7 3-D Mixed Oxide (MOX) Fuel Assembly Benchmark was modeled to test the unstructured mesh capabilities on a reactor-type problem.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗