### Abstract

Original language | English |
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Title of host publication | Proceedings |

Subtitle of host publication | International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013 |

Pages | 973-984 |

Publication status | Published - 2013 |

MoE publication type | Not Eligible |

Event | International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013 - Sun Valley, ID, United States Duration: 5 May 2013 → 9 May 2013 |

### Publication series

Name | |
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Publisher | Idaho National Laboratory |

Volume | 2 |

### Conference

Conference | International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013 |
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Abbreviated title | M&C 2013 |

Country | United States |

City | Sun Valley, ID |

Period | 5/05/13 → 9/05/13 |

### Fingerprint

### Keywords

- best rational approximation
- burnup equations
- CRAM
- serpent

### Cite this

*Proceedings: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013*(pp. 973-984)

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*Proceedings: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013.*pp. 973-984, International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C 2013, Sun Valley, ID, United States, 5/05/13.

**Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations.** / Pusa, Maria.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations

AU - Pusa, Maria

PY - 2013

Y1 - 2013

N2 - The burnup equations can in principle be solved by computing the exponential of the burnup matrix. However, due to the difficult numerical characteristics of burnup matrices, the problem is extremely stiff and the matrix exponential solution has previously been considered infeasible for an entire burnup system containing over a thousand nuclides. It was recently discovered by the author that the eigenvalues of burnup matrices are generally located near the negative real axis, which prompted introducing the Chebyshev rational approximation method (CRAM) for solving the burnup equations. CRAM can be characterized as the best rational approximation on the negative real axis and it has been shown to be capable of simultaneously solving an entire burnup system both accurately and efficiently. In this paper, the accuracy of CRAM is further studied in the context of burnup equations. The approximation error is analyzed based on the eigenvalue decomposition of the burnup matrix. It is deduced that the relative accuracy of CRAM may be compromised if a nuclide concentration diminishes significantly during the considered time step. Numerical results are presented for two test cases, the first one representing a small burnup system with 36 nuclides and the second one a full a decay system with 1531 nuclides.

AB - The burnup equations can in principle be solved by computing the exponential of the burnup matrix. However, due to the difficult numerical characteristics of burnup matrices, the problem is extremely stiff and the matrix exponential solution has previously been considered infeasible for an entire burnup system containing over a thousand nuclides. It was recently discovered by the author that the eigenvalues of burnup matrices are generally located near the negative real axis, which prompted introducing the Chebyshev rational approximation method (CRAM) for solving the burnup equations. CRAM can be characterized as the best rational approximation on the negative real axis and it has been shown to be capable of simultaneously solving an entire burnup system both accurately and efficiently. In this paper, the accuracy of CRAM is further studied in the context of burnup equations. The approximation error is analyzed based on the eigenvalue decomposition of the burnup matrix. It is deduced that the relative accuracy of CRAM may be compromised if a nuclide concentration diminishes significantly during the considered time step. Numerical results are presented for two test cases, the first one representing a small burnup system with 36 nuclides and the second one a full a decay system with 1531 nuclides.

KW - best rational approximation

KW - burnup equations

KW - CRAM

KW - serpent

M3 - Conference article in proceedings

SN - 978-0-89448-700-2

SP - 973

EP - 984

BT - Proceedings

ER -