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Franke, Brian C.

Publications and source records attributed to Franke, Brian C..

11 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A New Galerkin Quadrature Method Not Requiring a Matrix Inverse

We derive a new Galerkin quadrature (GQ) method for S 𝑛 calculations that differs from the two methods preceding it in that a matrix inverse for an 𝑁 𝑑 Γ— 𝑁 𝑑 matrix, where 𝑁𝑑 is the number of directions in the quadrature set, is no longer required. Galerkin quadrature methods are designed for calculations with highly anisotropic scattering. Such methods are not simply special angular quadratures but also are methods for representing the S 𝑛 scattering source that offers several advantages relative to the standard scattering source representation when highly truncated Legendre cross-section expansions must be used. Galerkin quadrature methods are also useful when the scattering is moderately anisotropic, but the quadrature being used is not sufficiently accurate for the order of the scattering source expansion that is required. Furthermore, we derive the new method and present computational results showing that its performance for two challenging problems is comparable to those of the two GQ methods that preceded it.

Galerkin quadrature↗
DOE OSTI2024

A Stochastic Calculus Approach to Boltzmann Transport

Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within source iteration are associated with the adjoint flux density and the adjoint particle paths are associated with the flux density. Here, we make our assertion rigorous through the use of stochastic calculus by representing the particle path used in source iteration as a solution to a stochastic differential equation (SDE). The solution to the adjoint Boltzmann equation is then expressed in terms of the same SDE, and the solution to the Boltzmann equation is expressed in terms of the SDE associated with the adjoint particle process. An important consequence is that the particle paths used within source iteration simultaneously provide Monte Carlo samples of the flux density and adjoint flux density in the detector and source regions, respectively. The significant practical implication is that particle trajectories can be reused to obtain both forward and adjoint quantities of interest. To the best our knowledge, the reuse of entire particles paths has not appeared in the literature. Monte Carlo simulations are presented to support the reuse of the particle paths.

Boltzmann transport↗
DOE OSTI2024

Qualitative Conditions for Reasonable Estimates of Kerma Using Total and Kerma Cross Section Attenuation of Photons

Performing a full adjoint simulation in the Integrated Tiger Series (ITS) can be time consuming to obtain statistically significant results. The ray-trace capability in ITS allows for rapid scoping calculations of the uncollided kerma from photon sources without needing to run a full adjoint simulation. However, the uncollided estimate will always underestimate the full-physics kerma since it neglects scattered radiation, and under certain conditions, the result from the capability may not provide a sufficiently accurate estimate of the full-physics kerma. To exemplify the conditions in which the capability provides reasonable estimates, two problem geometries with different materials are simulated using the full adjoint capability as well as the ray-trace capability with a total cross section treatment and a new kerma-attenuation cross-section treatment. The results are then compared to show under which conditions the estimates are accurate. Reasonable estimates are provided from the ray-trace feature when there is minimal scattering into a region of interest occurring, such as with low-Z material and when the photons travel through small amounts of material.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Use of Kerma for Subzone Dimension Specification in Monte Carlo Based Photon Energy Deposition Calculations

A technique using the photon kerma cross section for a material in combination with the number fraction from a photon energy spectrum has been developed to determine the estimated subzone dimension needed to provide an energy deposition profile in radiation transport calculations. The technique was verified using the ITS code for monoenergetic photon sources and a selection of photon spectra. A Python script was written to use the CEPXS cross-section file with a Rapture calculated transmission spectrum to provide the dimensional estimates in a rapid fashion. The script is available for SNL users through the corporate gitlab server.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

ITS Version 6.7: The Integrated TIGER Series of Coupled Electron/Photon Monte Carlo Transport Codes User's Manual

ITS is a powerful software package permitting state-of-the-art Monte Carlo solution of linear time-independent coupled electron/photon radiation transport problems, with or without the presence of macroscopic electric and magnetic fields of arbitrary spatial dependence. Our goal has been to simultaneously maximize operational simplicity and physical accuracy. Through a set of preprocessor directives, the user selects one of the many ITS codes. The ease with which the make system is applied combines with an input scheme based on order-independent descriptive keywords that makes maximum use of defaults and internal error checking to provide experimentalists and theorists alike with a method for the routine but rigorous solution of sophisticated radiation transport problems. Physical rigor is provided by employing accurate cross sections, sampling distributions, and physical models for describing the production and transport of the electron/photon cascade from 1.0 GeV down to 1.0 keV. The availability of source code permits the more sophisticated user to tailor the codes to specific applications and to extend the capabilities of the codes to more complex applications. Version 6, the latest version of ITS, contains (1) improvements to the ITS 5.0 codes, and (2) conversion to Fortran 95. The general user friendliness of the software has been enhanced through memory allocation to reduce the need for users to modify and recompile the code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Sensitivity Analyses for Monte Carlo Sampling-Based Particle Simulations

Computational design-based optimization is a well-used tool in science and engineering. Our report documents the successful use of a particle sensitivity analysis for design-based optimization within Monte Carlo sampling-based particle simulationβ€”a currently unavailable capability. Such a capability enables the particle simulation communities to go beyond forward simulation and promises to reduce the burden on overworked analysts by getting more done with less computation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Neuromorphic scaling advantages for energy-efficient random walk computations

Neuromorphic computing, which aims to replicate the computational structure and architecture of the brain in synthetic hardware, has typically focused on artificial intelligence applications. What is less explored is whether such brain-inspired hardware can provide value beyond cognitive tasks. Here we show that the high degree of parallelism and configurability of spiking neuromorphic architectures makes them well suited to implement random walks via discrete-time Markov chains. Overall, these random walks are useful in Monte Carlo methods, which represent a fundamental computational tool for solving a wide range of numerical computing tasks. Using IBM’s TrueNorth and Intel’s Loihi neuromorphic computing platforms, we show that our neuromorphic computing algorithm for generating random walk approximations of diffusion offers advantages in energy-efficient computation compared with conventional approaches. We also show that our neuromorphic computing algorithm can be extended to more sophisticated jump-diffusion processes that are useful in a range of applications, including financial economics, particle physics and machine learning.

97 MATHEMATICS AND COMPUTING↗