Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations

Maria Pusa

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

3 Citations (Scopus)

Abstract

The burnup equations can in principle be solved by computing the exponential of the burnup matrix. However, due to the difficult numerical characteristics of burnup matrices, the problem is extremely stiff and the matrix exponential solution has previously been considered infeasible for an entire burnup system containing over a thousand nuclides. It was recently discovered by the author that the eigenvalues of burnup matrices are generally located near the negative real axis, which prompted introducing the Chebyshev rational approximation method (CRAM) for solving the burnup equations. CRAM can be characterized as the best rational approximation on the negative real axis and it has been shown to be capable of simultaneously solving an entire burnup system both accurately and efficiently. In this paper, the accuracy of CRAM is further studied in the context of burnup equations. The approximation error is analyzed based on the eigenvalue decomposition of the burnup matrix. It is deduced that the relative accuracy of CRAM may be compromised if a nuclide concentration diminishes significantly during the considered time step. Numerical results are presented for two test cases, the first one representing a small burnup system with 36 nuclides and the second one a full a decay system with 1531 nuclides.
Original languageEnglish
Title of host publicationProceedings
Subtitle of host publicationInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013
Pages973-984
Publication statusPublished - 2013
MoE publication typeNot Eligible
EventInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013 - Sun Valley, ID, United States
Duration: 5 May 20139 May 2013

Publication series

Name
PublisherIdaho National Laboratory
Volume2

Conference

ConferenceInternational Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013
Abbreviated titleM&C 2013
CountryUnited States
CitySun Valley, ID
Period5/05/139/05/13

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Isotopes
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Keywords

  • best rational approximation
  • burnup equations
  • CRAM
  • serpent

Cite this

Pusa, M. (2013). Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations. In Proceedings: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013 (pp. 973-984)
Pusa, Maria. / Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations. Proceedings: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013. 2013. pp. 973-984
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Pusa, M 2013, Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations. in Proceedings: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013. pp. 973-984, International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013, Sun Valley, ID, United States, 5/05/13.

Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations. / Pusa, Maria.

Proceedings: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013. 2013. p. 973-984.

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

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Pusa M. Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations. In Proceedings: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013. 2013. p. 973-984