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Title: 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 end-of-step solution by dividing a step into equidistant sub-steps. 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:
 [1];  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Aalto Univ., Otaniemi (Finland)
  2. 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:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 183; Journal Issue: 1; Journal ID: ISSN 0029-5639
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/NSE15-67.
Isotalo, Aarno, & Pusa, Maria. Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps. United States. doi:10.13182/NSE15-67.
Isotalo, Aarno, and Pusa, Maria. Sun . "Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps". United States. doi:10.13182/NSE15-67. 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 end-of-step solution by dividing a step into equidistant sub-steps. 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/NSE15-67},
journal = {Nuclear Science and Engineering},
number = 1,
volume = 183,
place = {United States},
year = {2016},
month = {5}
}

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Works referenced in this record:

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