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A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems.

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Title: A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems.
Authors: Xu, Tianshi1 (AUTHOR) tianshi.xu@emory.edu, Li, Rui Peng2 (AUTHOR), Osei-Kuffuor, Daniel2 (AUTHOR)
Source: International Journal of High Performance Computing Applications. May2025, Vol. 39 Issue 3, p424-442. 19p.
Subjects: Algebraic multigrid methods, Sparse matrices, Krylov subspace, Parallel processing, Linear systems
Abstract: This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of High Performance Computing Applications is the property of Sage Publications Inc. 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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DbLabel: Engineering Source
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  Data: A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems.
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  Data: <searchLink fieldCode="AR" term="%22Xu%2C+Tianshi%22">Xu, Tianshi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> tianshi.xu@emory.edu</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Rui+Peng%22">Li, Rui Peng</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Osei-Kuffuor%2C+Daniel%22">Osei-Kuffuor, Daniel</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+High+Performance+Computing+Applications%22">International Journal of High Performance Computing Applications</searchLink>. May2025, Vol. 39 Issue 3, p424-442. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Algebraic+multigrid+methods%22">Algebraic multigrid methods</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+matrices%22">Sparse matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Krylov+subspace%22">Krylov subspace</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel+processing%22">Parallel processing</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of High Performance Computing Applications is the property of Sage Publications Inc. 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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        Value: 10.1177/10943420251319334
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      – Code: eng
        Text: English
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        PageCount: 19
        StartPage: 424
    Subjects:
      – SubjectFull: Algebraic multigrid methods
        Type: general
      – SubjectFull: Sparse matrices
        Type: general
      – SubjectFull: Krylov subspace
        Type: general
      – SubjectFull: Parallel processing
        Type: general
      – SubjectFull: Linear systems
        Type: general
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      – TitleFull: A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems.
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            NameFull: Li, Rui Peng
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            – D: 01
              M: 05
              Text: May2025
              Type: published
              Y: 2025
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            – TitleFull: International Journal of High Performance Computing Applications
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