Solving eigenvalue response matrix equations with nonlinear techniques
This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response...
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| Format: | Article |
| Language: | en_US |
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Elsevier
2017
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| Online Access: | http://hdl.handle.net/1721.1/108255 https://orcid.org/0000-0003-1459-7672 |
| _version_ | 1826200788847820800 |
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| author | Roberts, Jeremy Alyn Forget, Benoit Robert Yves |
| author2 | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Roberts, Jeremy Alyn Forget, Benoit Robert Yves |
| author_sort | Roberts, Jeremy Alyn |
| collection | MIT |
| description | This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k -eigenvalue via balance, while the inner λλ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λλ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov–Schur method applied to the λλ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness. |
| first_indexed | 2024-09-23T11:41:27Z |
| format | Article |
| id | mit-1721.1/108255 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:41:27Z |
| publishDate | 2017 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1082552022-10-01T05:21:16Z Solving eigenvalue response matrix equations with nonlinear techniques Roberts, Jeremy Alyn Forget, Benoit Robert Yves Massachusetts Institute of Technology. Department of Nuclear Science and Engineering forget benoit Roberts, Jeremy Alyn Forget, Benoit Robert Yves This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k -eigenvalue via balance, while the inner λλ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λλ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov–Schur method applied to the λλ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness. United States. Department of Energy (Nuclear Energy University Programs Graduate Fellowshi) 2017-04-19T17:05:30Z 2017-04-19T17:05:30Z 2014-02 2014-02 Article http://purl.org/eprint/type/JournalArticle 03064549 http://hdl.handle.net/1721.1/108255 Roberts, Jeremy A., and Benoit Forget. “Solving Eigenvalue Response Matrix Equations with Nonlinear Techniques.” Annals of Nuclear Energy 69 (July 2014): 97–107. https://orcid.org/0000-0003-1459-7672 en_US http://dx.doi.org/10.1016/j.anucene.2014.02.002 Annals of Nuclear Energy Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier Prof. Forget via Chris Sherratt |
| spellingShingle | Roberts, Jeremy Alyn Forget, Benoit Robert Yves Solving eigenvalue response matrix equations with nonlinear techniques |
| title | Solving eigenvalue response matrix equations with nonlinear techniques |
| title_full | Solving eigenvalue response matrix equations with nonlinear techniques |
| title_fullStr | Solving eigenvalue response matrix equations with nonlinear techniques |
| title_full_unstemmed | Solving eigenvalue response matrix equations with nonlinear techniques |
| title_short | Solving eigenvalue response matrix equations with nonlinear techniques |
| title_sort | solving eigenvalue response matrix equations with nonlinear techniques |
| url | http://hdl.handle.net/1721.1/108255 https://orcid.org/0000-0003-1459-7672 |
| work_keys_str_mv | AT robertsjeremyalyn solvingeigenvalueresponsematrixequationswithnonlineartechniques AT forgetbenoitrobertyves solvingeigenvalueresponsematrixequationswithnonlineartechniques |