863
Views
2
CrossRef citations to date
0
Altmetric
Technical Papers

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

ORCID Icon, &
Pages 558-588 | Received 07 Jun 2022, Accepted 23 Sep 2022, Published online: 09 Dec 2022

REFERENCES

  • H. BATEMAN, “Solution of a System of Differential Equations Occurring in the Theory of Radioactive Transformations,” Proc. Camb. Philos. Soc., Math. Phys. Eng., 15, 423 (1910).
  • G. I. BELL and S. GLASSTONE, Nuclear Reactor Theory, Litton Educational Publishing (1970).
  • C. MOLER and C. V. LOAN, “Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later,” Soc. Ind. Appl. Math. Rev., 45, 1, 3 (2003).
  • M. PUSA and J. LEPPÄNEN, “Computing the Matrix Exponential in Burnup Calculations,” Nucl. Sci. Eng., 164, 2, 140 (2010); https://doi.org/10.13182/NSE09-14.
  • M. PUSA, “Rational Approximations to the Matrix Exponential in Burnup Calculations,” Nucl. Sci. Eng., 169, 2, 155 (2011); https://doi.org/10.13182/NSE10-81.
  • J. LEPPÄNEN et al., “The Serpent Monte Carlo Code: Status, Development and Applications in 2013,” Ann. Nucl. Energy, 82, 142 (2015); https://doi.org/10.1016/j.anucene.2014.08.024.
  • O. W. HERMANN and R. M. WESTFALL, “ORIGEN-S: SCALE System Module to Calculate Fuel Depletion, Actinide Transmutation, Fission Product Buildup and Decay, and Associated Radiation Source Terms,” in “SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluation,” NUREG/CR-0200, Vol II, Sec. F7, U.S. Nuclear Regulatory Commission (1998).
  • J. ORTENSI et al., “Griffin Software Development Plan,” INL/EXT-21-63185, ANL/NSE-21/23, Idaho National Laboratory and Argonne National Laboratory (2021); https://doi.org/10.2172/1845956.
  • O. CALVIN et al., “Implementation of Depletion Architecture in the MAMMOTH Reactor Physics Application,” Proc. 2019 Int. Conf. Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Portland, Oregon, August 25–29, 2019, p. 2806, American Nuclear Society (2019).
  • M. PUSA and J. LEPPÄNEN, “Solving Linear Systems with Sparse Gaussian Elimination in the Chebyshev Rational Approximation Method,” Nucl. Sci. Eng., 175, 3, 250 (2013); https://doi.org/10.13182/NSE12-52.
  • M. PUSA, “Higher-Order Chebyshev Rational Approximation Method and Application to Burnup Equations,” Nucl. Sci. Eng., 182, 3, 297 (2016); https://doi.org/10.13182/NSE15-26.
  • O. CALVIN, S. SCHUNERT, and B. GANAPOL, “Global Error Analysis of the Chebyshev Rational Approximation Method,” Ann. Nucl. Energy, 150, 107828 (2021); https://doi.org/10.1016/j.anucene.2020.107828.
  • E. ANDERSON et al., “LAPACK Users’ Guide,” Society for Industrial and Applied Mathematics (1999).
  • G. MARLEAU, A. HEBERT, and R. ROY, “A User Guide for DRAGON Version 5,” User Manual IGE-355, Ecole Polytechnique de Montreal (2018).
  • D. BROWN et al., “ENDF/B-VIII.0: The 8th Major Release of the Nuclear Reaction Data Library with CIELO-Project Cross Sections, New Standards and Thermal Scattering Data,” Nucl. Data Sheets, 148, 1, (2018); https://doi.org/10.1016/j.nds.2018.02.001.
  • “Benchmark for Neutronic Analysis of Sodium-Cooled Fast Reactor Cores with Various Fuel Types and Core Sizes,” NEA/NSC/R(2015)9, Organisation for Economic Co-operation and Development, Nuclear Energy Agency (2016).