Stochastic methods for uncertainty quantification in radiation transport

American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009

Volumn 4, Issue , 2009, Pages 2380-2394

  Fichtl, Erin D ^a   Prinja, Anil K ^b   Warsa, James S ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b MSC01 1070   (United States)

Author keywords

Polynomial chaos expansions; Radiation transport; Uncertainty quantification

Indexed keywords

CROSS SECTION; DETERMINISTIC TRANSPORT; EIGEN-VALUE; FIXED SOURCE PROBLEM; FULLY-COUPLED; GALERKIN PROJECTIONS; GENERALIZED POLYNOMIAL CHAOS (GPC); MONTE CARLO; NEWTON KRYLOV METHOD; NON-LINEAR; ORTHOGONAL BASIS; ORTHOGONAL POLYNOMIAL; PARAMETER UNCERTAINTY; PERTURBATION METHOD; POLYNOMIAL CHAOS EXPANSION; QUADRATURE RULES; RADIATION TRANSPORT; SAMPLING-BASED; SECOND ORDERS; SOLUTION METHODS; SPECTRAL EXPANSIONS; STOCHASTIC COLLOCATION METHOD; STOCHASTIC FINITE-ELEMENT METHOD; STOCHASTIC METHODS; UNCERTAINTY QUANTIFICATIONS;

CHAOS THEORY; COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; POLYNOMIALS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; RANDOM VARIABLES; STOCHASTIC SYSTEMS;

PERTURBATION TECHNIQUES;

EID: 74549191369     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (11)

1. I. Babuska, F. Nobile, and R. Tempone. A stochastic collocation method for elliptic partial differential equations with random input data. SIAM Journal on Numerical Analysis, 45(3): 1005-1034, 2007.
2. A.F. Emery. Some thoughts on solving the radiative transfer equation in stochastic media using polynomial chaos and wick products as applied to radiative equilibrium. Journal of Quantitative Spectroscopy and Radiative Transfer, 93(1-3):61-77, June 2005.
3. R. Ghanem and P. Spanos. Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, New York, 1991.
4. R. Koekoek and R.F. Swarttouw. The askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. Technical Report 94-05, TU Delft, Delft, The Netherlands, 1994.
5. L. Mathelin, M.Y. Hussaini, and T.A. Zang. Stochastic approaches to uncertainty quantification in cfd simulations. Numerical Algorithms, 38(1-3):209-236, 2005.
6. C.J. Sallaberry, J.C. Helton, and S.C. Hora. Extension of latin hypercube samples with correlated variables. Reliability Engineering and System Safety, 93(7): 1047-1059, July 2008.
7. A. Sood, R.A. Forster, and D.K. Parsons. Analytical benchmark test set for criticality code verification. Progress in Nuclear Energy, 42(1):55-106, 2003.
8. N. Wiener. The homogeneous chaos. American Journal of Mathematics, 60(4):897-936, October 1938.
9. M.M.R. Williams. Polynomial chaos functions and stochastic differential equations. Annals of Nuclear Energy, 33(9):774-785, June 2006.
10. D. Xiu and J.S. Hesthaven. High-order collocation methods for differential equations with random inputs. SIAM Journal on Scientific Computing, 27(3): 1118-1139, 2005.
11. D. Xiu and G.E. Karniadakis. The wiener-askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing, 24(2):619-644, 2002.