Uncertainty Quantification For Multigroup Diffusion Equations Using Sparse Tensor Approximations
Fuenzalida
C
author
Jerez-Hanckes
C
author
McClarren
R
G
author
2019
English
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.
multigroup diffusion equation
uncertainty quantification
sparse tensor approximation
finite element method
WOS:000473033300033
exported from refbase (show.php?record=1023), last updated on Wed, 14 Aug 2019 22:08:42 -0400
text
10.1137/18M1185995
Fuenzalida_etal2019
Siam Journal On Scientific Computing
SIAM J. Sci. Comput.
2019
Siam Publications
continuing
periodical
academic journal
41
3
B545-B575
1064-8275