Abstract
The topic of this paper is solving the burnup equations using dedicated
matrix exponential methods that are based on two different types of
rational approximation near the negative real axis. The previously
introduced Chebyshev Rational Approximation Method (CRAM) is now
analyzed in detail for its accuracy and convergence, and correct partial
fraction coefficients for approximation orders 14 and 16 are given to
facilitate its implementation and improve the accuracy. As a new
approach, rational approximation based on quadrature formulas derived
from complex contour integrals is proposed, which forms an attractive
alternative to CRAM, as its coefficients are easy to compute for any
order of approximation. This gives the user the option to routinely
choose between computational efficiency and accuracy all the way up to
the level permitted by the available arithmetic precision. The presented
results for two test cases are validated against reference solutions
computed using high-precision arithmetics. The observed behavior of the
methods confirms the previous conclusions of CRAM’s excellent
suitability for burnup calculations and establishes the quadrature-based
approximation as a viable and flexible alternative that, like CRAM, has
its foundation in the specific eigenvalue properties of burnup
matrices.
Original language | English |
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Pages (from-to) | 155-167 |
Journal | Nuclear Science and Engineering |
Volume | 169 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2011 |
MoE publication type | A1 Journal article-refereed |