Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations

Abstract

In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the eigenvalue and left and right eigenvectors. The practical computation of these estimators requires the estimation of a constant called prefactor, which we can express as the spectral norm of some operator. We provide some elements of theoretical analysis which illustrate the link between the expression of the prefactor we obtain here and its well-known expression in the case of symmetric eigenvalue problems, either using the notion of numerical range of the operator, or via a perturbative analysis. Lastly, we propose a practical method in order to estimate this prefactor which yields interesting numerical results on actual test cases. We provide detailed numerical simulations on two-dimensional examples including a multigroup neutron diffusion equation.
Fichier principal
Vignette du fichier
main (1).pdf (1.17 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

cea-04156959 , version 1 (10-07-2023)

Identifiers

  • HAL Id : cea-04156959 , version 1

Cite

Yonah Conjungo Taumhas, Geneviève Dusson, Virginie Ehrlacher, Tony Lelièvre, François Madiot. Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations. 2023. ⟨cea-04156959⟩
143 View
93 Download

Share

Gmail Mastodon Facebook X LinkedIn More