• NUCLEAR TECHNIQUES
  • Vol. 47, Issue 2, 020604 (2024)
Zhaocai XIANG, Qiafeng CHEN, Pengcheng ZHAO*, and Qinghang ZHANG
Author Affiliations
  • School of Nuclear Science and Technology, University of South China, Hengyang 421001, China
  • show less
    DOI: 10.11889/j.0253-3219.2024.hjs.47.020604 Cite this Article
    Zhaocai XIANG, Qiafeng CHEN, Pengcheng ZHAO, Qinghang ZHANG. Apply implicitly restarted Arnoldi method to solving eigenvalue problem and reducing dimensionality in neutron diffusion[J]. NUCLEAR TECHNIQUES, 2024, 47(2): 020604 Copy Citation Text show less
    References

    [1] XIE Zhongsheng, YI Banghua[M]. Physical analysis of nuclear reactors-volume I(1994).

    [2] JIANG Yaolin[M]. Model reduction method, 1-7(2010).

    [3] HUANG Yichao, ZHANG Shaohong. Implicitly restarted Arnoldi method and its application to the solution of higher order harmonics[J]. Chinese Journal of Nuclear Science and Engineering, 28, 102-106(2008).

    [4] WANG Changhui, WU Hongchun, CAO Liangzhi. Harmonics expansion method for on-line monitoring of PWR power distribution[J]. Nuclear Power Engineering, 31, 97-101(2010).

    [5] XIE Jinsen, ZHAO Shouzhi, YU Tao et al. Harmonics calculation and analysis of λ and prompt α eigenvalue problems for slab reactor based on the implicitly restarted arnoldi methods[J]. Journal of University of South China (Science and Technology), 30, 9-13(2016).

    [6] Pearson K. On lines and planes of closest fit to systems of points in space[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2, 559-572(1901).

    [7] Hotelling H. Analysis of a complex of statistical variables into principal components[J]. Journal of Educational Psychology, 24, 417-441(1933).

    [8] Sirovich L. Turbulence and the dynamics of coherent structures. III. Dynamics and scaling[J]. Quarterly of Applied Mathematics, 45, 583-590(1987).

    [9] Buchan A G, Pain C C, Fang F et al. A POD reduced-order model for eigenvalue problems with application to reactor physics[J]. International Journal for Numerical Methods in Engineering, 95, 1011-1032(2013).

    [10] Sartori A, Baroli D, Cammi A et al. Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics[J]. Annals of Nuclear Energy, 71, 217-229(2014).

    [11] YANG Junhe. Application of OpenFOAM in neutron transport calculation and its order reduction[D](2019).

    [12] WANG Li, MIAO Zhen, JIANG Yaolin. Model order reduction based on Galerkin KPOD for partial differential equations with variable coefficients[J]. Journal on Numerical Methods and Computer Applications, 42, 226-236(2021).

    [13] Sorensen D C. Implicit application of polynomial filters in akstep Arnoldi method[J]. Siam Journal on Matrix Analysis and Applications, 13, 357-385(1992).

    [14] CHENG Tao. Research on eigenmode theory and its fast algorithm[D](2022).

    [15] Ge J, Zhang D L, Tian W X et al. Steady and transient solutions of neutronics problems based on finite volume method (FVM) with a CFD code[J]. Progress in Nuclear Energy, 85, 366-374(2015).

    Zhaocai XIANG, Qiafeng CHEN, Pengcheng ZHAO, Qinghang ZHANG. Apply implicitly restarted Arnoldi method to solving eigenvalue problem and reducing dimensionality in neutron diffusion[J]. NUCLEAR TECHNIQUES, 2024, 47(2): 020604
    Download Citation