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Nuclear Science and Engineering
Fusion Science and Technology
Finding fusion’s place
Fusion energy is attracting significant interest from governments and private capital markets. The deployment of fusion energy on a timeline that will affect climate change and offer another tool for energy security will require support from stakeholders, regulators, and policymakers around the world. Without broad support, fusion may fail to reach its potential as a “game-changing” technology to make a meaningful difference in addressing the twin challenges of climate change and geopolitical energy security.
The process of developing the necessary policy and regulatory support is already underway around the world. Leaders in the United States, the United Kingdom, the European Union, China, and elsewhere are engaging with the key issues and will lead the way in setting the foundation for a global fusion industry.
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.