A POD reduced‐order model for eigenvalue problems with application to reactor physics. (3rd July 2013)

• Record Type: Journal Article
• Authors: Buchan, A. G.; Pain, C. C.; Fang, F.; Navon, I. M.
• Is Part Of: International journal for numerical methods in engineering. Volume 95:Number 12(2013)
• Page Start: 1011
• Page End: 1032
• Publication Date: 2013-07-03
• Subjects: POD -- reduced‐order modelling -- eigenvalue problem -- reactor criticality; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4533
• Languages: English
• ISSNs: 0029-5981

Abstract

SUMMARY: A reduced‐order model based on proper orthogonal decomposition (POD) has been presented and applied to solving eigenvalue problems. The model is constructed via the method of snapshots, which is based upon the singular value decomposition of a matrix containing the characteristics of a solution as it evolves through time. Part of the novelty of this work is in how this snapshot data are generated, and this is through the recasting of eigenvalue problem, which is time independent, into a time‐dependent form. Instances of time‐dependent eigenfunction solutions are therefore used to construct the snapshot matrix. The reduced order model's capabilities in efficiently resolving eigenvalue problems that typically become computationally expensive (using standard full model discretisations) has been demonstrated. Although the approach can be adapted to most general eigenvalue problems, the examples presented here are based on calculating dominant eigenvalues in reactor physics applications. The approach is shown to reconstruct both the eigenvalues and eigenfunctions accurately using a significantly reduced number of unknowns in comparison with 'full' models based on finite element discretisations. The novelty of this paper therefore includes a new approach to generating snapshots, POD's application to large‐scale eigenvalue calculations, and reduced‐order model's application in reactor physics.Copyright © 2013 John Wiley & Sons, Ltd.