Monte Carlo Solution of k-Eigenvalue Problem Using Subspace Iteration Method.
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| Title: | Monte Carlo Solution of k-Eigenvalue Problem Using Subspace Iteration Method. |
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| Authors: | Gupta, Anurag1,2 anurag@barc.gov.in, Modak, R. S.3 |
| Source: | Nuclear Science & Engineering. Feb2020, Vol. 194 Issue 2, p87-103. 17p. |
| Subjects: | Eigenvalues, Subspaces (Mathematics), Monte Carlo method |
| Abstract: | Monte Carlo calculations for the evaluation of fundamental mode solution of k-eigenvalue problems generally make use of the Power Iteration (PI) method, which suffers from poor convergence, particularly in the case of large, loosely coupled systems. In the present paper, a method called Meyer's Subspace Iteration (SSI) method, also called the Simultaneous vector iteration algorithm, is applied for the Monte Carlo solution of the k-eigenvalue problem. The SSI method is the block generalization of the single-vector PI method and has been found to work efficiently for solving the problem with the deterministic neutron transport setup. It is found that the convergence of the fundamental k-eigenvalue and corresponding fission source distribution improves substantially with the SSI-based Monte Carlo method as compared to the PI-based Monte Carlo method. To reduce the extra computational effort needed for simultaneous iterations with several vectors, a novel procedure is adopted in which it takes almost the same effort as with the single-vector PI-based Monte Carlo method. The algorithm is applied to several one-dimensional slab test cases of varying difficulty, and the results are compared with the standard PI method. It is observed that unlike the PI method, the SSI-based Monte Carlo method converges quickly and does not require many inactive generations before the mean and variance of eigenvalues could be estimated. It has been demonstrated that the SSI method can simultaneously find a set of the most dominant higher k-eigenmodes in addition to the fundamental mode solution. [ABSTRACT FROM AUTHOR] |
| Copyright of Nuclear Science & Engineering is the property of Taylor & Francis Ltd 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 141048570 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Monte Carlo Solution of k-Eigenvalue Problem Using Subspace Iteration Method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gupta%2C+Anurag%22">Gupta, Anurag</searchLink><relatesTo>1,2</relatesTo><i> anurag@barc.gov.in</i><br /><searchLink fieldCode="AR" term="%22Modak%2C+R%2E+S%2E%22">Modak, R. S.</searchLink><relatesTo>3</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Nuclear+Science+%26+Engineering%22">Nuclear Science & Engineering</searchLink>. Feb2020, Vol. 194 Issue 2, p87-103. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Subspaces+%28Mathematics%29%22">Subspaces (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Monte Carlo calculations for the evaluation of fundamental mode solution of k-eigenvalue problems generally make use of the Power Iteration (PI) method, which suffers from poor convergence, particularly in the case of large, loosely coupled systems. In the present paper, a method called Meyer's Subspace Iteration (SSI) method, also called the Simultaneous vector iteration algorithm, is applied for the Monte Carlo solution of the k-eigenvalue problem. The SSI method is the block generalization of the single-vector PI method and has been found to work efficiently for solving the problem with the deterministic neutron transport setup. It is found that the convergence of the fundamental k-eigenvalue and corresponding fission source distribution improves substantially with the SSI-based Monte Carlo method as compared to the PI-based Monte Carlo method. To reduce the extra computational effort needed for simultaneous iterations with several vectors, a novel procedure is adopted in which it takes almost the same effort as with the single-vector PI-based Monte Carlo method. The algorithm is applied to several one-dimensional slab test cases of varying difficulty, and the results are compared with the standard PI method. It is observed that unlike the PI method, the SSI-based Monte Carlo method converges quickly and does not require many inactive generations before the mean and variance of eigenvalues could be estimated. It has been demonstrated that the SSI method can simultaneously find a set of the most dominant higher k-eigenmodes in addition to the fundamental mode solution. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Nuclear Science & Engineering is the property of Taylor & Francis Ltd 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/00295639.2019.1668655 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 87 Subjects: – SubjectFull: Eigenvalues Type: general – SubjectFull: Subspaces (Mathematics) Type: general – SubjectFull: Monte Carlo method Type: general Titles: – TitleFull: Monte Carlo Solution of k-Eigenvalue Problem Using Subspace Iteration Method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gupta, Anurag – PersonEntity: Name: NameFull: Modak, R. S. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 00295639 Numbering: – Type: volume Value: 194 – Type: issue Value: 2 Titles: – TitleFull: Nuclear Science & Engineering Type: main |
| ResultId | 1 |
