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 language | English |
|---|---|
| Title of host publication | Proceedings |
| Subtitle of host publication | International Conference on the Physics of Reactors 2012: Advances in Reactor Physics, PHYSOR 2012 |
| Publisher | American Nuclear Society (ANS) |
| Pages | 952-963 |
| Volume | 2 |
| ISBN (Print) | 978-1-6227-6389-4 |
| Publication status | Published - 2012 |
| MoE publication type | A4 Article in a conference publication |
| Event | International Conference on the Physics of Reactors, PHYSOR 2012: Advances in Reactor Physics - Knoxville, United States Duration: 15 Apr 2012 → 20 Apr 2012 |
Conference
| Conference | International Conference on the Physics of Reactors, PHYSOR 2012 |
|---|---|
| Country/Territory | United States |
| City | Knoxville |
| Period | 15/04/12 → 20/04/12 |
Keywords
- Burnup equations
- Chebyshev Rational Approximation Method
- CRAM
- serpent