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Author (up) Fuenzalida, C.; Jerez-Hanckes, C.; McClarren, R.G. doi  openurl
  Title Uncertainty Quantification For Multigroup Diffusion Equations Using Sparse Tensor Approximations Type Journal Article
  Year 2019 Publication Siam Journal On Scientific Computing Abbreviated Journal SIAM J. Sci. Comput.  
  Volume 41 Issue 3 Pages B545-B575  
  Keywords multigroup diffusion equation; uncertainty quantification; sparse tensor approximation; finite element method  
  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.  
  Address [Fuenzalida, Consuelo] Pontificia Univ Catolica Chile, Sch Engn, Santiago, Chile, Email: mcfuenzalida@uc.cl;  
  Corporate Author Thesis  
  Publisher Siam Publications Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1064-8275 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000473033300033 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 1023  
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