Computing the Matrix Exponential in Burnup Calculations

Maria Pusa, Jaakko Leppänen

    Research output: Contribution to journalArticleScientificpeer-review

    112 Citations (Scopus)

    Abstract

    The topic of this paper is the computation of the matrix exponential in the context of burnup equations. The established matrix exponential methods are introduced briefly. The eigenvalues of the burnup matrix are important in choosing the matrix exponential method, and their characterization is considered. Based on the characteristics of the burnup matrix, the Chebyshev rational approximation method (CRAM) and its interpretation as a numeric contour integral are discussed in detail. The introduced matrix exponential methods are applied to two test cases representing an infinite pressurized water reactor pin-cell lattice, and the numerical results are presented. The results suggest that CRAM is capable of providing a robust and accurate solution to the burnup equations with a very short computation time.
    Original languageEnglish
    Pages (from-to)140-150
    Number of pages11
    JournalNuclear Science and Engineering
    Volume164
    Issue number2
    DOIs
    Publication statusPublished - 2010
    MoE publication typeA1 Journal article-refereed

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    Pressurized water reactors

    Cite this

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    title = "Computing the Matrix Exponential in Burnup Calculations",
    abstract = "The topic of this paper is the computation of the matrix exponential in the context of burnup equations. The established matrix exponential methods are introduced briefly. The eigenvalues of the burnup matrix are important in choosing the matrix exponential method, and their characterization is considered. Based on the characteristics of the burnup matrix, the Chebyshev rational approximation method (CRAM) and its interpretation as a numeric contour integral are discussed in detail. The introduced matrix exponential methods are applied to two test cases representing an infinite pressurized water reactor pin-cell lattice, and the numerical results are presented. The results suggest that CRAM is capable of providing a robust and accurate solution to the burnup equations with a very short computation time.",
    author = "Maria Pusa and Jaakko Lepp{\"a}nen",
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    doi = "10.13182/NSE09-14",
    language = "English",
    volume = "164",
    pages = "140--150",
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    }

    Computing the Matrix Exponential in Burnup Calculations. / Pusa, Maria; Leppänen, Jaakko.

    In: Nuclear Science and Engineering, Vol. 164, No. 2, 2010, p. 140-150.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

    T1 - Computing the Matrix Exponential in Burnup Calculations

    AU - Pusa, Maria

    AU - Leppänen, Jaakko

    PY - 2010

    Y1 - 2010

    N2 - The topic of this paper is the computation of the matrix exponential in the context of burnup equations. The established matrix exponential methods are introduced briefly. The eigenvalues of the burnup matrix are important in choosing the matrix exponential method, and their characterization is considered. Based on the characteristics of the burnup matrix, the Chebyshev rational approximation method (CRAM) and its interpretation as a numeric contour integral are discussed in detail. The introduced matrix exponential methods are applied to two test cases representing an infinite pressurized water reactor pin-cell lattice, and the numerical results are presented. The results suggest that CRAM is capable of providing a robust and accurate solution to the burnup equations with a very short computation time.

    AB - The topic of this paper is the computation of the matrix exponential in the context of burnup equations. The established matrix exponential methods are introduced briefly. The eigenvalues of the burnup matrix are important in choosing the matrix exponential method, and their characterization is considered. Based on the characteristics of the burnup matrix, the Chebyshev rational approximation method (CRAM) and its interpretation as a numeric contour integral are discussed in detail. The introduced matrix exponential methods are applied to two test cases representing an infinite pressurized water reactor pin-cell lattice, and the numerical results are presented. The results suggest that CRAM is capable of providing a robust and accurate solution to the burnup equations with a very short computation time.

    U2 - 10.13182/NSE09-14

    DO - 10.13182/NSE09-14

    M3 - Article

    VL - 164

    SP - 140

    EP - 150

    JO - Nuclear Science and Engineering

    JF - Nuclear Science and Engineering

    SN - 0029-5639

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