Issue |
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
|
|
---|---|---|
Page(s) | 1959 - 1987 | |
DOI | https://doi.org/10.1051/m2an/2024055 | |
Published online | 21 October 2024 |
Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations
1
Université Paris-Saclay, CEA, Service d’Études des Réacteurs et de Mathématiques Appliquées, 91191 Gif-sur-Yvette, France
2
Laboratoire de Mathématiques de Besancon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon, France
3
CERMICS Ecole des Ponts, and MATHERIALS project-team Inria, 6-8 avenue Blaise Pascal, 77455 Marne-la-Vallée, France
* Corresponding author: francois.madiot@cea.fr
Received:
5
July
2023
Accepted:
3
July
2024
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 smallest eigenvalue which is assumed to be simple and the associated 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.
Mathematics Subject Classification: 65N15 / 65N25 / 65N30 / 82D75
Key words: Neutronics / diffusion equation / reduced basis
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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