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

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 soluti...

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Veröffentlicht in:International journal for numerical methods in engineering Jg. 95; H. 12; S. 1011 - 1032
Hauptverfasser: Buchan, A. G., Pain, C. C., Fang, F., Navon, I. M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Chichester Blackwell Publishing Ltd 21.09.2013
Wiley
Wiley Subscription Services, Inc
Schlagworte:
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
Critical system
Karhunen Loeve transformation
POD
Eigenfunction
Dominance
Modeling
Nuclear reactor
reactor criticality
Finite element method
Time dependence
Problem solving
Eigenvalue problem
Reduced order systems
reduced-order modelling
Large scale
Reduced order model
Principal component analysis
Singular value decomposition
Novelty
ISSN:0029-5981, 1097-0207
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Zusammenfassung: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.
Bibliographie:istex:DB3E366D485D275E20802F0CEFEAE0ECB7515B63
EPSRC - No. EP/J002011/1
ArticleID:NME4533
ark:/67375/WNG-QGHRF73F-T
NSF - No. ATM-0931198
ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4533