Uncertainty quantification for multigroup diffusion equations using sparse tensor approximations

Consuelo Fuenzalida, Carlos Jerez-Hanckes, Ryan G. McClarren

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)B545-B575
JournalSIAM Journal on Scientific Computing
Issue number3
StatePublished - 2019
Externally publishedYes


  • Finite element method
  • Multigroup diffusion equation
  • Sparse tensor approximation
  • Uncertainty quantification


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