An efficient implementation of the Chebyshev Rational Approximation Method (CRAM) for solving the burnup equations

Maria Pusa, Jaakko Leppänen

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

    6 Citations (Scopus)

    Abstract

    The Chebyshev Rational Approximation Method (CRAM) has been recently introduced by the authors for solving the burnup equations with excellent results. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method only requires a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on considering the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstrated by computing the CRAM approximations for a large test case with over 1600 nuclides
    Original languageEnglish
    Title of host publicationProceedings
    Subtitle of host publicationInternational Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012
    PublisherAmerican Nuclear Society ANS
    Pages952-963
    Volume2
    ISBN (Print)978-1-6227-6389-4
    Publication statusPublished - 2012
    MoE publication typeA4 Article in a conference publication
    EventInternational Conference on the Physics of Reactors, PHYSOR 2012: Advances in Reactor Physics - Knoxville, United States
    Duration: 15 Apr 201220 Apr 2012

    Conference

    ConferenceInternational Conference on the Physics of Reactors, PHYSOR 2012
    CountryUnited States
    CityKnoxville
    Period15/04/1220/04/12

    Fingerprint

    Isotopes
    Factorization
    Linear systems

    Keywords

    • Burnup equations
    • Chebyshev Rational Approximation Method
    • CRAM
    • serpent

    Cite this

    Pusa, M., & Leppänen, J. (2012). An efficient implementation of the Chebyshev Rational Approximation Method (CRAM) for solving the burnup equations. In Proceedings: International Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012 (Vol. 2, pp. 952-963). American Nuclear Society ANS.
    Pusa, Maria ; Leppänen, Jaakko. / An efficient implementation of the Chebyshev Rational Approximation Method (CRAM) for solving the burnup equations. Proceedings: International Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012. Vol. 2 American Nuclear Society ANS, 2012. pp. 952-963
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    abstract = "The Chebyshev Rational Approximation Method (CRAM) has been recently introduced by the authors for solving the burnup equations with excellent results. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method only requires a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on considering the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstrated by computing the CRAM approximations for a large test case with over 1600 nuclides",
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    Pusa, M & Leppänen, J 2012, An efficient implementation of the Chebyshev Rational Approximation Method (CRAM) for solving the burnup equations. in Proceedings: International Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012. vol. 2, American Nuclear Society ANS, pp. 952-963, International Conference on the Physics of Reactors, PHYSOR 2012, Knoxville, United States, 15/04/12.

    An efficient implementation of the Chebyshev Rational Approximation Method (CRAM) for solving the burnup equations. / Pusa, Maria; Leppänen, Jaakko.

    Proceedings: International Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012. Vol. 2 American Nuclear Society ANS, 2012. p. 952-963.

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

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    Pusa M, Leppänen J. An efficient implementation of the Chebyshev Rational Approximation Method (CRAM) for solving the burnup equations. In Proceedings: International Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012. Vol. 2. American Nuclear Society ANS. 2012. p. 952-963