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

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Název: An Efficient and Robust ILU(k) Preconditioner for Steady-State Neutron Diffusion Problem Based on MOOSE
Autoři: Yingjie Wu, Han Zhang, Lixun Liu, Huanran Tang, Qinrong Dou, Jiong Guo, Fu Li
Zdroj: Energies, Vol 17, Iss 6, p 1499 (2024)
Informace o vydavateli: MDPI AG
Rok vydání: 2024
Sbírka: Directory of Open Access Journals: DOAJ Articles
Témata: preconditioning, JFNK, coloring algorithm, reordering algorithm, incomplete LU factorization, Technology
Popis: 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.
Druh dokumentu: article in journal/newspaper
Jazyk: English
Relation: https://www.mdpi.com/1996-1073/17/6/1499; https://doaj.org/toc/1996-1073; https://doaj.org/article/4e075d27f2474547bcaf3f851040e811
DOI: 10.3390/en17061499
Dostupnost: https://doi.org/10.3390/en17061499
https://doaj.org/article/4e075d27f2474547bcaf3f851040e811
Přístupové číslo: edsbas.EC6EDA92
Databáze: BASE
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: An Efficient and Robust ILU(k) Preconditioner for Steady-State Neutron Diffusion Problem Based on MOOSE
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  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Yingjie+Wu%22">Yingjie Wu</searchLink><br /><searchLink fieldCode="AR" term="%22Han+Zhang%22">Han Zhang</searchLink><br /><searchLink fieldCode="AR" term="%22Lixun+Liu%22">Lixun Liu</searchLink><br /><searchLink fieldCode="AR" term="%22Huanran+Tang%22">Huanran Tang</searchLink><br /><searchLink fieldCode="AR" term="%22Qinrong+Dou%22">Qinrong Dou</searchLink><br /><searchLink fieldCode="AR" term="%22Jiong+Guo%22">Jiong Guo</searchLink><br /><searchLink fieldCode="AR" term="%22Fu+Li%22">Fu Li</searchLink>
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  Data: Energies, Vol 17, Iss 6, p 1499 (2024)
– Name: Publisher
  Label: Publisher Information
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  Data: MDPI AG
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2024
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  Data: Directory of Open Access Journals: DOAJ Articles
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  Data: <searchLink fieldCode="DE" term="%22preconditioning%22">preconditioning</searchLink><br /><searchLink fieldCode="DE" term="%22JFNK%22">JFNK</searchLink><br /><searchLink fieldCode="DE" term="%22coloring+algorithm%22">coloring algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22reordering+algorithm%22">reordering algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22incomplete+LU+factorization%22">incomplete LU factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Technology%22">Technology</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: 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.
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  Data: article in journal/newspaper
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  Data: https://www.mdpi.com/1996-1073/17/6/1499; https://doaj.org/toc/1996-1073; https://doaj.org/article/4e075d27f2474547bcaf3f851040e811
– Name: DOI
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  Group: ID
  Data: 10.3390/en17061499
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  Data: https://doi.org/10.3390/en17061499<br />https://doaj.org/article/4e075d27f2474547bcaf3f851040e811
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    Subjects:
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        Type: general
      – SubjectFull: JFNK
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      – SubjectFull: coloring algorithm
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      – SubjectFull: reordering algorithm
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      – SubjectFull: incomplete LU factorization
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      – TitleFull: An Efficient and Robust ILU(k) Preconditioner for Steady-State Neutron Diffusion Problem Based on MOOSE
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