A Limited-Memory Framework for Conditional Point Sampling for Radiation Transport in 1D Stochastic Media

Abstract

Conditional Point Sampling (CoPS) is our newly proposed Monte Carlo method for transport in stochastic media that has been demonstrated to achieve highly accurate mean response results and to compute variance of the mean caused by random spatial mixing. The ability of CoPS to efficiently characterize the effects of random spatial mixing beyond the mean is hindered by the algorithm’s potentially unbounded computer memory footprint. Thus, in previous work, we established two limited-memory techniques for CoPS to improve required computer memory, i.e., recent memory (RM) CoPS and amnesia radius (AR) CoPS, the latter of which enables CoPS to tractably compute probability density functions (PDFs) of response. In this work, we create a limited-memory framework that allows CoPS to combine the advantages of limited-memory techniques and populate the framework with the two inaugural techniques of RM and AR. The proposed framework enables the user to control the computational performance of CoPS by making problem-specific trade-offs between accuracy, computer memory footprint, and characterization of response distributions based on input parameters. We present mean leakage results, material-dependent scalar flux, leakage PDFs, and computer memory footprint computed using this new framework. By selecting different input parameters in our proposed limited-memory framework, CoPS is demonstrated to roughly match the accuracy and computer memory footprint of the established approximate method Chord Length Sampling or to provide response distribution information comparable to the brute-force benchmark approach while improving the computer memory footprint compared to the original CoPS algorithm.

Keywords:

• Conditional Point Sampling
• stochastic media
• recent memory
• amnesia radius
• limited memory

Acknowledgments

This article has been authored by an employee of National Technology & Engineering Solutions of Sandia, LLC under Contract No. DE-NA0003525 with the U.S. Department of Energy (DOE). The employee owns all right, title and interest in and to the article and is solely responsible for its contents. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this article or allow others to do so, for United States Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan https://www.energy.gov/downloads/doe-public-access-plan. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the U.S. Department of Energy Nuclear Energy University Programs Graduate Fellowship and the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories, a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.