DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE

Emeline Rosier; Li Mao; Luiz Leal

doi:10.13182/M&C21-33732

DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE

Emeline Rosier, Li Mao, Luiz Leal

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

The subgroup method currently implemented in the APOLLO3^® lattice code relies on moment-based probability tables, also called mathematical probability tables. This paper details the on-the-fly construction of another kind of probability tables, known as physical probability tables, by conserving self-shielded cross sections over a range of dilutions with two different methods. The first is an already existing method in other lattice codes and consists of approximating the cross section with a Padé approximant, whose coefficients are determined with a linear system. The second method is an improvement of the first and relies on the use of orthogonal polynomials in order to get a linear system as diagonal as possible. The two methods are compared in this paper, their numerical errors and the possible improvements are highlighted.

Original language	English
Title of host publication	Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
Publisher	American Nuclear Society
Pages	1992-2001
Number of pages	10
ISBN (Electronic)	9781713886310
DOIs	https://doi.org/10.13182/M&C21-33732
State	Published - 2021
Externally published	Yes
Event	2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 - Virtual, Online Duration: Oct 3 2021 → Oct 7 2021

Publication series

Name	Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

Conference

Conference	2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
City	Virtual, Online
Period	10/3/21 → 10/7/21

Funding

The authors wish to express their appreciation and gratitude to Dr. Richard Sanchez for many fruitful discussions. APOLLO3® is a registered trademark of CEA. We gratefully acknowledge EDF and Framatome for their long term partnership and their support.

Keywords

Physical probability table
Self-shielding
Subgroup method

Access to Document

10.13182/M&C21-33732

Cite this

Rosier, E., Mao, L., & Leal, L. (2021). DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE. In Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 (pp. 1992-2001). (Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021). American Nuclear Society. https://doi.org/10.13182/M&C21-33732

Rosier, Emeline ; Mao, Li ; Leal, Luiz. / DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE. Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021. American Nuclear Society, 2021. pp. 1992-2001 (Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021).

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title = "DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE",

abstract = "The subgroup method currently implemented in the APOLLO3{\textregistered} lattice code relies on moment-based probability tables, also called mathematical probability tables. This paper details the on-the-fly construction of another kind of probability tables, known as physical probability tables, by conserving self-shielded cross sections over a range of dilutions with two different methods. The first is an already existing method in other lattice codes and consists of approximating the cross section with a Pad{\'e} approximant, whose coefficients are determined with a linear system. The second method is an improvement of the first and relies on the use of orthogonal polynomials in order to get a linear system as diagonal as possible. The two methods are compared in this paper, their numerical errors and the possible improvements are highlighted.",

keywords = "Physical probability table, Self-shielding, Subgroup method",

author = "Emeline Rosier and Li Mao and Luiz Leal",

note = "Publisher Copyright: Copyright {\textcopyright} 2021 AMERICAN NUCLEAR SOCIETY, INCORPORATED, LA GRANGE PARK, ILLINOIS 60526.All rights reserved.; 2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 ; Conference date: 03-10-2021 Through 07-10-2021",

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doi = "10.13182/M\&C21-33732",

language = "English",

series = "Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021",

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Rosier, E, Mao, L & Leal, L 2021, DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE. in Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021. Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021, American Nuclear Society, pp. 1992-2001, 2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021, Virtual, Online, 10/3/21. https://doi.org/10.13182/M&C21-33732

DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE. / Rosier, Emeline; Mao, Li; Leal, Luiz.
Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021. American Nuclear Society, 2021. p. 1992-2001 (Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Rosier, Emeline

AU - Mao, Li

AU - Leal, Luiz

PY - 2021

Y1 - 2021

N2 - The subgroup method currently implemented in the APOLLO3® lattice code relies on moment-based probability tables, also called mathematical probability tables. This paper details the on-the-fly construction of another kind of probability tables, known as physical probability tables, by conserving self-shielded cross sections over a range of dilutions with two different methods. The first is an already existing method in other lattice codes and consists of approximating the cross section with a Padé approximant, whose coefficients are determined with a linear system. The second method is an improvement of the first and relies on the use of orthogonal polynomials in order to get a linear system as diagonal as possible. The two methods are compared in this paper, their numerical errors and the possible improvements are highlighted.

AB - The subgroup method currently implemented in the APOLLO3® lattice code relies on moment-based probability tables, also called mathematical probability tables. This paper details the on-the-fly construction of another kind of probability tables, known as physical probability tables, by conserving self-shielded cross sections over a range of dilutions with two different methods. The first is an already existing method in other lattice codes and consists of approximating the cross section with a Padé approximant, whose coefficients are determined with a linear system. The second method is an improvement of the first and relies on the use of orthogonal polynomials in order to get a linear system as diagonal as possible. The two methods are compared in this paper, their numerical errors and the possible improvements are highlighted.

KW - Physical probability table

KW - Self-shielding

KW - Subgroup method

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BT - Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

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Rosier E, Mao L, Leal L. DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE. In Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021. American Nuclear Society. 2021. p. 1992-2001. (Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021). doi: 10.13182/M&C21-33732

DYNAMIC CONSTRUCTION OF PHYSICAL PROBABILITY TABLES FOR RESONANT MIXTURE

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