Uncertainty Quantification for Multigroup Diffusion Equations Using Sparse Tensor Approximations
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.
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Published In
SIAM Journal on Scientific Computing
Pages: B545 - B575
DOI: 10.1137/18M1185995
ISSN (online): 1095-7197
Copyright
© 2019, Society for Industrial and Applied Mathematics.
History
Submitted: 7 May 2018
Accepted: 3 April 2019
Published online: 20 June 2019
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Corporación de Fomento de la Producción https://doi.org/10.13039/100009465 : 201603
Fondo Nacional de Desarrollo Científico y Tecnológico https://doi.org/10.13039/501100002850 : 1171491
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- Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element ApproximationSIAM Journal on Scientific Computing, Vol. 42, No. 5 | 1 September 2020
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