UNCERTAINTY QUANTIFICATION FOR MULTIGROUP DIFFUSION EQUATIONS USING SPARSE TENSOR APPROXIMATIONS

Fuenzalida C.; Jerez-Hanckes C.; McClarren R.G.

Abstract

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.

Más información

Título según WOS: UNCERTAINTY QUANTIFICATION FOR MULTIGROUP DIFFUSION EQUATIONS USING SPARSE TENSOR APPROXIMATIONS
Título según SCOPUS: Uncertainty quantification for multigroup diffusion equations using sparse tensor approximations
Título de la Revista: SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volumen: 41
Número: 3
Editorial: SIAM PUBLICATIONS
Fecha de publicación: 2019
Página de inicio: B545
Página final: B575
Idioma: English
DOI:

10.1137/18M1185995

Notas: ISI, SCOPUS