A POD reduced-order model for eigenvalue problems with application to reactor physics

• Published in: International journal for numerical methods in engineering 2013-09, Vol.95 (12), p.1011-1032
• Main Authors: Buchan, A. G., Pain, C. C., Fang, F., Navon, I. M.
• Format: Article
• Language: English
• Subjects: Algebra; Applied sciences; Computational efficiency; Construction; Consumer goods; Eigenfunctions; eigenvalue problem; Eigenvalues; Energy; Energy. Thermal use of fuels; Exact sciences and technology; Fission nuclear power plants; Installations for energy generation and conversion: thermal and electrical energy; Linear and multilinear algebra, matrix theory; Mathematical analysis; Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; POD; reactor criticality; Reactor physics; reduced-order modelling; Sciences and techniques of general use
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4533

SUMMARYA 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.