TY - JOUR

T1 - Uncertainty quantification for multigroup diffusion equations using sparse tensor approximations

AU - Fuenzalida, Consuelo

AU - Jerez-Hanckes, Carlos

AU - McClarren, Ryan G.

N1 - Funding Information:
∗Submitted to the journal’s Computational Methods in Science and Engineering section May 7, 2018; accepted for publication (in revised form) April 3, 2019; published electronically June 20, 2019. http://www.siam.org/journals/sisc/41-3/M118599.html Funding: This work was partially supported by the Corfo 2030 Seed Fund Program TAMU-PUC 201603 and Fondecyt Regular 1171491. †School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile (mcfuenzalida@ uc.cl). ‡Faculty of Engineering and Sciences, Universidad Adolfo Ibañez, Santiago, Chile (carlos.jerez@uai.cl). §Department of Aerospace and Mechanical Engineering, College of Engineering, University of Notre Dame, Notre Dame, IN 46556 (rmcclarr@nd.edu).
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics

PY - 2019

Y1 - 2019

N2 - We develop a novel method to compute first and second order statistical moments of the neutron kinetic density inside a nuclear system by solving the energy-dependent neutron diffusion equation. Randomness comes from the lack of precise knowledge of external sources as well as of the interaction parameters, known as cross sections. Thus, the density is itself a random variable. As Monte Carlo simulations entail intense computational work, we are interested in deterministic approaches to quantify uncertainties. By assuming as given the first and second statistical moments of the excitation terms, a sparse tensor finite element approximation of the first two statistical moments of the dependent variables for each energy group can be efficiently computed in one run. Numerical experiments provided validate our derived convergence rates and point to further research avenues.

AB - We develop a novel method to compute first and second order statistical moments of the neutron kinetic density inside a nuclear system by solving the energy-dependent neutron diffusion equation. Randomness comes from the lack of precise knowledge of external sources as well as of the interaction parameters, known as cross sections. Thus, the density is itself a random variable. As Monte Carlo simulations entail intense computational work, we are interested in deterministic approaches to quantify uncertainties. By assuming as given the first and second statistical moments of the excitation terms, a sparse tensor finite element approximation of the first two statistical moments of the dependent variables for each energy group can be efficiently computed in one run. Numerical experiments provided validate our derived convergence rates and point to further research avenues.

KW - Finite element method

KW - Multigroup diffusion equation

KW - Sparse tensor approximation

KW - Uncertainty quantification

UR - http://www.scopus.com/inward/record.url?scp=85071837570&partnerID=8YFLogxK

U2 - 10.1137/18M1185995

DO - 10.1137/18M1185995

M3 - Article

AN - SCOPUS:85071837570

SN - 1064-8275

VL - 41

SP - B545-B575

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 3

ER -