Analysis of the Ill-Posedness in Subgroup Parameter Calculation Based on Pade Approximation and Research on Improved Methods

Yongfa Zhang, Song Li (), Lei Liu (), Xinwen Zhao, Qi Cai and Qian Zhang
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Yongfa Zhang: College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
Song Li: College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
Lei Liu: College of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China
Xinwen Zhao: College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
Qi Cai: College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
Qian Zhang: Laboratory for Advanced Nuclear Energy Theory and Applications, Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China

Mathematics, 2025, vol. 13, issue 16, 1-27

Abstract: This paper addresses the ill-posed problem in calculating subgroup parameters for resonance self-shielding within nuclear reactor physics. The conventional Pade approximation method often yields negative subgroup cross-sections lacking physical meaning due to its treatment of overdetermined nonlinear systems, making the subgroup transport equations unsolvable. To overcome this, an optimized Pade approximation method is proposed: a resonance factor criterion is used to select energy groups requiring calculation; a systematic procedure dynamically traverses background cross-section combinations starting from a minimal subgroup number, incrementally increasing it until solutions meeting accuracy constraints with positive parameters are found; and, given the insufficiency of background points, a high-resolution resonance integral table is constructed, particularly for ranges exhibiting significant cross-section variations. Numerical validation confirms the method eliminates negative parameters, ensures physical validity, and significantly improves accuracy across benchmark cases including typical fuel pins, burnt pellets, and Gd-bearing lattices. This approach effectively resolves the ill-posedness of the traditional method, offering a more robust and precise subgroup resonance treatment for high-fidelity core neutronics.

Keywords: subgroup method; Pade approximation; subgroup parameter; resonance self-shielding treatment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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