Hyper‐Reduced Model Based on the Proper Orthogonal Decomposition and the LU Factorization Applied to the Neutron Diffusion Eigenvalue Problem.
Saved in:
| Title: | Hyper‐Reduced Model Based on the Proper Orthogonal Decomposition and the LU Factorization Applied to the Neutron Diffusion Eigenvalue Problem. |
|---|---|
| Authors: | Vidal‐Ferràndiz, A.1 (AUTHOR) anvifer2@upv.es, Carreño, A.2 (AUTHOR), Javaloyas, E.2 (AUTHOR), Ginestar, D.1 (AUTHOR), Verdú, G.2 (AUTHOR) |
| Source: | International Journal for Numerical Methods in Engineering. 2/15/2026, Vol. 127 Issue 3, p1-20. 20p. |
| Subjects: | Proper orthogonal decomposition, Neutron diffusion, Reduced-order models, Matrix decomposition, Eigenvalues, Optimization algorithms |
| Abstract: | An efficient method for solving large eigenvalue problems efficiently can be developed using hyper‐reduced order models, such as those arising from the LU Proper Orthogonal Decomposition (LUPOD). The LUPOD employs dominant orthogonal modes along with a flexible number of collocation points to establish a reduced scalar product, thereby enhancing computational efficiency to construct the reduced order model. This strategy produces accurate results when a similar number of collocation points and orthogonal modes are used. For problems where the number of available modes is small due to the high computational cost of its computation or because sufficient model accuracy can be achieved with less data, LUPOD may not yield enough precise results. This work proposes an extension of the LUPOD method to increase the number of collocation points in the reduced scalar product and consequently, the accuracy of the LUPOD. The performance of this method is illustrated with a diffusion‐reaction problem with analytical solution. Then, this method is applied to solve the neutron diffusion eigenvalue problem. Numerical results for these methodologies are tested for obtaining the k‐effective and the steady‐state neutron flux distribution of three‐dimensional nuclear reactor benchmark problems. They show that using 20 snapshots and 40% of the mesh points of the problem as collocation points speeds up the simulations by about 100 times with respect to the resolution of the full order eigenvalue problem while maintaining accurate results that differ by less than 100 pcm in the eigenvalue and less than 1.2% in the neutron flux determination. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 191491099 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Hyper‐Reduced Model Based on the Proper Orthogonal Decomposition and the LU Factorization Applied to the Neutron Diffusion Eigenvalue Problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Vidal‐Ferràndiz%2C+A%2E%22">Vidal‐Ferràndiz, A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> anvifer2@upv.es</i><br /><searchLink fieldCode="AR" term="%22Carreño%2C+A%2E%22">Carreño, A.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Javaloyas%2C+E%2E%22">Javaloyas, E.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ginestar%2C+D%2E%22">Ginestar, D.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Verdú%2C+G%2E%22">Verdú, G.</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+for+Numerical+Methods+in+Engineering%22">International Journal for Numerical Methods in Engineering</searchLink>. 2/15/2026, Vol. 127 Issue 3, p1-20. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Proper+orthogonal+decomposition%22">Proper orthogonal decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Neutron+diffusion%22">Neutron diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22Reduced-order+models%22">Reduced-order models</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+decomposition%22">Matrix decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: An efficient method for solving large eigenvalue problems efficiently can be developed using hyper‐reduced order models, such as those arising from the LU Proper Orthogonal Decomposition (LUPOD). The LUPOD employs dominant orthogonal modes along with a flexible number of collocation points to establish a reduced scalar product, thereby enhancing computational efficiency to construct the reduced order model. This strategy produces accurate results when a similar number of collocation points and orthogonal modes are used. For problems where the number of available modes is small due to the high computational cost of its computation or because sufficient model accuracy can be achieved with less data, LUPOD may not yield enough precise results. This work proposes an extension of the LUPOD method to increase the number of collocation points in the reduced scalar product and consequently, the accuracy of the LUPOD. The performance of this method is illustrated with a diffusion‐reaction problem with analytical solution. Then, this method is applied to solve the neutron diffusion eigenvalue problem. Numerical results for these methodologies are tested for obtaining the k‐effective and the steady‐state neutron flux distribution of three‐dimensional nuclear reactor benchmark problems. They show that using 20 snapshots and 40% of the mesh points of the problem as collocation points speeds up the simulations by about 100 times with respect to the resolution of the full order eigenvalue problem while maintaining accurate results that differ by less than 100 pcm in the eigenvalue and less than 1.2% in the neutron flux determination. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=191491099 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/nme.70272 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 1 Subjects: – SubjectFull: Proper orthogonal decomposition Type: general – SubjectFull: Neutron diffusion Type: general – SubjectFull: Reduced-order models Type: general – SubjectFull: Matrix decomposition Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Optimization algorithms Type: general Titles: – TitleFull: Hyper‐Reduced Model Based on the Proper Orthogonal Decomposition and the LU Factorization Applied to the Neutron Diffusion Eigenvalue Problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Vidal‐Ferràndiz, A. – PersonEntity: Name: NameFull: Carreño, A. – PersonEntity: Name: NameFull: Javaloyas, E. – PersonEntity: Name: NameFull: Ginestar, D. – PersonEntity: Name: NameFull: Verdú, G. IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 02 Text: 2/15/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00295981 Numbering: – Type: volume Value: 127 – Type: issue Value: 3 Titles: – TitleFull: International Journal for Numerical Methods in Engineering Type: main |
| ResultId | 1 |
