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

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Title: An Efficient and Robust ILU(k) Preconditioner for Steady-State Neutron Diffusion Problem Based on MOOSE.
Authors: Wu, Yingjie1 (AUTHOR) wuyingjie@tsinghua.edu.cn, Zhang, Han1 (AUTHOR) han-zhang@tsinghua.edu.cn, Liu, Lixun1 (AUTHOR), Tang, Huanran1 (AUTHOR), Dou, Qinrong1 (AUTHOR), Guo, Jiong1 (AUTHOR), Li, Fu1 (AUTHOR)
Source: Energies (19961073). Mar2024, Vol. 17 Issue 6, p1499. 16p.
Subjects: Neutron diffusion, Matrix decomposition, Moose, Nuclear engineering, Finite differences, Neutron transport theory
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. [ABSTRACT FROM AUTHOR]
Copyright of Energies (19961073) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  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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  Data: <searchLink fieldCode="AR" term="%22Wu%2C+Yingjie%22">Wu, Yingjie</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wuyingjie@tsinghua.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Han%22">Zhang, Han</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> han-zhang@tsinghua.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Lixun%22">Liu, Lixun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tang%2C+Huanran%22">Tang, Huanran</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Dou%2C+Qinrong%22">Dou, Qinrong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Guo%2C+Jiong%22">Guo, Jiong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Fu%22">Li, Fu</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Energies+%2819961073%29%22">Energies (19961073)</searchLink>. Mar2024, Vol. 17 Issue 6, p1499. 16p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Neutron+diffusion%22">Neutron diffusion</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+decomposition%22">Matrix decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Moose%22">Moose</searchLink><br /><searchLink fieldCode="DE" term="%22Nuclear+engineering%22">Nuclear engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+differences%22">Finite differences</searchLink><br /><searchLink fieldCode="DE" term="%22Neutron+transport+theory%22">Neutron transport theory</searchLink>
– Name: Abstract
  Label: Abstract
  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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Energies (19961073) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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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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              Text: Mar2024
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