Stochastic methods for uncertainty quantification in radiation transport

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The use of generalized polynomial chaos (gPC) expansions is investigated for uncertainty quantification in radiation transport. The gPC represents second-order random processes in terms of an expansion of orthogonal polynomials of random variables and is used to represent the uncertain input(s) and unknown(s). We assume a single uncertain input-the total macroscopic cross section-although this does not represent a limitation of the approaches considered here. Two solution methods are examined: The Stochastic Finite Element Method (SFEM) and the Stochastic Collocation Method (SCM). The SFEM entails taking Galerkin projections onto the orthogonal basis, which, for fixed source problems, yields a linear system ... continued below

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Fichtl, Erin D; Prinja, Anil K & Warsa, James S January 1, 2009.

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The use of generalized polynomial chaos (gPC) expansions is investigated for uncertainty quantification in radiation transport. The gPC represents second-order random processes in terms of an expansion of orthogonal polynomials of random variables and is used to represent the uncertain input(s) and unknown(s). We assume a single uncertain input-the total macroscopic cross section-although this does not represent a limitation of the approaches considered here. Two solution methods are examined: The Stochastic Finite Element Method (SFEM) and the Stochastic Collocation Method (SCM). The SFEM entails taking Galerkin projections onto the orthogonal basis, which, for fixed source problems, yields a linear system of fully -coupled equations for the PC coefficients of the unknown. For k-eigenvalue calculations, the SFEM system is non-linear and a Newton-Krylov method is employed to solve it. The SCM utilizes a suitable quadrature rule to compute the moments or PC coefficients of the unknown(s), thus the SCM solution involves a series of independent deterministic transport solutions. The accuracy and efficiency of the two methods are compared and contrasted. The PC coefficients are used to compute the moments and probability density functions of the unknown(s), which are shown to be accurate by comparing with Monte Carlo results. Our work demonstrates that stochastic spectral expansions are a viable alternative to sampling-based uncertainty quantification techniques since both provide a complete characterization of the distribution of the flux and the k-eigenvalue. Furthermore, it is demonstrated that, unlike perturbation methods, SFEM and SCM can handle large parameter uncertainty.

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  • Int. Conference on Mathematics, Computational Methods & Reactor Physics ; May 3, 2009 ; Saratoga Springs, NY

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  • Report No.: LA-UR-09-01151
  • Report No.: LA-UR-09-1151
  • Grant Number: AC52-06NA25396
  • Office of Scientific & Technical Information Report Number: 956465
  • Archival Resource Key: ark:/67531/metadc935548

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  • January 1, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 5:08 p.m.

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Fichtl, Erin D; Prinja, Anil K & Warsa, James S. Stochastic methods for uncertainty quantification in radiation transport, article, January 1, 2009; [New Mexico]. (digital.library.unt.edu/ark:/67531/metadc935548/: accessed April 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.