Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps
Abstract
The Chebyshev Rational Approximation Method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any endofstep solution by dividing a step into equidistant substeps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the LU decompositions for the linear solves required in CRAM only need to be formed on the first substep. The improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. Lastly, with substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.
 Authors:

 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Aalto Univ., Otaniemi (Finland)
 VTT Technical Research Centre of Finland, Espoo (Finland)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE; Finnish Research Program
 OSTI Identifier:
 1362192
 Grant/Contract Number:
 AC0500OR22725
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 183; Journal Issue: 1; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society  Taylor & Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEAR CHEMISTRY; CRAM; substeps; depletion; decay
Citation Formats
Isotalo, Aarno, and Pusa, Maria. Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps. United States: N. p., 2016.
Web. doi:10.13182/NSE1567.
Isotalo, Aarno, & Pusa, Maria. Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps. United States. doi:10.13182/NSE1567.
Isotalo, Aarno, and Pusa, Maria. Sun .
"Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps". United States. doi:10.13182/NSE1567. https://www.osti.gov/servlets/purl/1362192.
@article{osti_1362192,
title = {Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps},
author = {Isotalo, Aarno and Pusa, Maria},
abstractNote = {The Chebyshev Rational Approximation Method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any endofstep solution by dividing a step into equidistant substeps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the LU decompositions for the linear solves required in CRAM only need to be formed on the first substep. The improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. Lastly, with substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.},
doi = {10.13182/NSE1567},
journal = {Nuclear Science and Engineering},
number = 1,
volume = 183,
place = {United States},
year = {2016},
month = {5}
}
Web of Science
Works referenced in this record:
Isotopic Depletion and Decay Methods and Analysis Capabilities in SCALE
journal, May 2011
 Gauld, Ian C.; Radulescu, Georgeta; Ilas, Germina
 Nuclear Technology, Vol. 174, Issue 2
Comparison of depletion algorithms for large systems of nuclides
journal, February 2011
 Isotalo, A. E.; Aarnio, P. A.
 Annals of Nuclear Energy, Vol. 38, Issue 23
Nineteen Dubious Ways to Compute the Exponential of a Matrix, TwentyFive Years Later
journal, January 2003
 Moler, Cleve; Van Loan, Charles
 SIAM Review, Vol. 45, Issue 1
Computing the Matrix Exponential in Burnup Calculations
journal, February 2010
 Pusa, Maria; Leppänen, Jaakko
 Nuclear Science and Engineering, Vol. 164, Issue 2