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Fusion Science and Technology
By the time you read this, I will have celebrated my 41st anniversary as a member of the American Nuclear Society. In thinking about this time, I find myself realizing that I have never been part of anything else (besides my immediate family) for as long. I joined ANS when I started graduate school and have been an active member ever since. In that time, I have worked for several employers, been active in other professional and social organizations, lived in four different states, and worked on projects that have taken me all over the world—but my ties to ANS and the people I have met here have been the most influential I have ever known. In thinking about this, I can only come to one conclusion: there is something special about ANS. Is it the technology? The people? For me, it is both.
Maria Pusa, Jaakko Leppänen
Nuclear Science and Engineering | Volume 175 | Number 3 | November 2013 | Pages 250-258
Technical Paper | dx.doi.org/10.13182/NSE12-52
Articles are hosted by Taylor and Francis Online.
The Chebyshev Rational Approximation Method (CRAM) has recently been introduced by the authors to solve burnup equations, and the results have been excellent. 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 requires only 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 consideration of 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 1606 nuclides.