An Efficient and Robust ILU(k) Preconditioner for Steady-State Neutron Diffusion Problem Based on MOOSE

Yingjie Wu, Han Zhang (), Lixun Liu, Huanran Tang, Qinrong Dou, Jiong Guo and Fu Li
Additional contact information
Yingjie Wu: Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China
Han Zhang: Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China
Lixun Liu: Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China
Huanran Tang: Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China
Qinrong Dou: Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China
Jiong Guo: Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China
Fu Li: Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China

Energies, 2024, vol. 17, issue 6, 1-16

Abstract: Jacobian-free Newton Krylov (JFNK) is an attractive method to solve nonlinear equations in the nuclear engineering community, and has been successfully applied to steady-state neutron diffusion k-eigenvalue problems and multi-physics coupling problems. Preconditioning technique plays an important role in the JFNK algorithm, significantly affecting its computational efficiency. The key point is how to automatically construct a high-quality preconditioning matrix that can improve the convergence rate and perform the preconditioning matrix factorization efficiently and robustly. A reordering-based ILU(k) preconditioner is proposed to achieve the above objectives. In detail, the finite difference technique combined with the coloring algorithm is utilized to automatically construct a preconditioning matrix with low computational cost . Furthermore, the reordering algorithm is employed for the ILU(k) to reduce the additional non-zero elements and pursue robust computational performance. A 2D LRA neutron steady-state benchmark problem is used to evaluate the performance of the proposed preconditioning technique, and a steady-state neutron diffusion k-eigenvalue problem with thermal-hydraulic feedback is also utilized as a supplement. The results show that coloring algorithms can automatically and efficiently construct the preconditioning matrix. The computational efficiency of the FDP with coloring could be about 60 times higher than that of the preconditioner without the coloring algorithm. The reordering-based ILU(k) preconditioner shows excellent robustness, avoiding the effect of the fill-in level k choice in incomplete LU factorization. Moreover, its performances under different fill-in levels are comparable to the optimal computational cost with natural ordering.

Keywords: preconditioning; JFNK; coloring algorithm; reordering algorithm; incomplete LU factorization (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1996-1073/17/6/1499/pdf (application/pdf)
https://www.mdpi.com/1996-1073/17/6/1499/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:17:y:2024:i:6:p:1499-:d:1361257

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().