Research on the Iterative Method for Solving Neutron Diffusion Equation

Fang Chao; Li Qing; Peng Xingjie; Zhao Wenbo; Liu Kun; Chen Zhang; Wang Lianjie

doi:10.13832/j.jnpe.2025.S1.0021

Volume 46 Issue S1

Jul. 2025

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Fang Chao, Li Qing, Peng Xingjie, Zhao Wenbo, Liu Kun, Chen Zhang, Wang Lianjie. Research on the Iterative Method for Solving Neutron Diffusion Equation[J]. Nuclear Power Engineering, 2025, 46(S1): 21-25. doi: 10.13832/j.jnpe.2025.S1.0021

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Fang Chao, Li Qing, Peng Xingjie, Zhao Wenbo, Liu Kun, Chen Zhang, Wang Lianjie. Research on the Iterative Method for Solving Neutron Diffusion Equation[J]. Nuclear Power Engineering, 2025, 46(S1): 21-25. doi: 10.13832/j.jnpe.2025.S1.0021

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Research on the Iterative Method for Solving Neutron Diffusion Equation

doi: 10.13832/j.jnpe.2025.S1.0021

Fang Chao^{1, 2
,
,},
Li Qing^{1, 3},
Peng Xingjie^{1, 3},
Zhao Wenbo^{1, 2},
Liu Kun^{1, 2},
Chen Zhang^{1, 2},
Wang Lianjie^{1, 2}

1.
Nuclear Power Institute of China, Chengdu, 610213, China
2.
National Key Laboratory of Nuclear Reactor Technology, Nuclear Power Institute of China, Chengdu, 610213, China
3.
State Key Laboratory of Advanced Nuclear Energy Technology, Nuclear Power Institute of China, Chengdu, 610213, China

Received Date: 2025-02-19
Rev Recd Date: 2025-04-13
Publish Date: 2025-07-09

Abstract

Abstract

To improve the computational efficiency of solving the eigenvalue of the neutron diffusion equation, this paper conducts an in-depth research on the power iteration method and the eigenvalue iteration algorithm based on the Krylov subspace idea. Firstly, in the power iteration method, an initial value setting based on fission source normalization is proposed and compared with the traditional method. Then, the number of iterations and computation time of the power iteration method and Kroylov-based iteration algorithm are compared. Finally, the preconditioning techniques of Kroylov-based iterative method are studied, including the Jacobian preconditioning, incomplete LU decomposition preconditioning, and algebraic multigrid preconditioning, and their impact on the number of iterations and computation time are analyzed. Through the calculation of the IAEA 3D benchmark problem, the results show that the Davidson type iterative algorithm combined with incomplete LU decomposition preconditioning has superior computational efficiency. For a problem with two million elements, the calculation can be completed within one minute by using a single core. Compared with traditional power iteration methods, the computational efficiency is improved by about 25 times. This achievement has significantly enhanced the computational efficiency of eigenvalue problems of the neutron diffusion equation and remarkably reduced the time cost of neutronics calculations.
- Neutron diffusion equation,
- Finite element method,
- Krylov method,
- Davidson method,
- Preconditioning technique

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References(9)

References

[1]	吉恩·戈卢布,查尔斯·范洛恩. 矩阵计算[M]. 程晓亮,译. 北京: 人民邮电出版社,2020: 487-493.
[2]	ZHAO W B, CHAI X M, ZHANG B, et al. A nodal method based on CMFD for pin-by-pin SP3 calculation[J]. Annals of Nuclear Energy, 2022, 167: 108849. doi: 10.1016/j.anucene.2021.108849
[3]	ROMERO E, ROMAN J E. A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc[J]. ACM Transactions on Mathematical Software, 2014, 40(2): 13.
[4]	KIRK B S, PETERSON J W, STOGNER R H, et al. libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations[J]. Engineering with Computers, 2006, 22(3-4): 237-254. doi: 10.1007/s00366-006-0049-3
[5]	ROMAN E, CAMPOS C, ROMERO E, et al. SLEPc users manual: DSIC-Ⅱ/24/02-Revision 3.12[R]. Valencia, Spain: Universitat of Politecnica de Valencia, 2019.
[6]	李治刚,安萍,贺涛,等. 基于中子扩散方程的JFNK方法研究[J]. 核动力工程,2019, 40(S2): 67-73.
[7]	戴小英,高兴誉,周爱辉. 特征值问题的Davidson型方法及其实现技术[J]. 数值计算与计算机应用,2006, 27(3): 218-240. doi: 10.3969/j.issn.1000-3266.2006.03.008
[8]	BALAY S, ABHYANKAR S, ADAMS M, et al, PETSc users manual: ANL-95/11 – Revision 3.8[R]. Argonne: Argonne National Laboratory, 2017.
[9]	Argonne Code Center. Benchmark problem book: ANL-7416[R]. La Grange Park, Illinois: Computational Benchmark Problems Committee of the Mathematics and Computation Division of the American Nuclear Society, 1977.