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A Non‐Nested Mesh Perspective on Highly Parallel Multilevel Schwarz Preconditioner.

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Title: A Non‐Nested Mesh Perspective on Highly Parallel Multilevel Schwarz Preconditioner.
Authors: Ma, Chengdi1 (AUTHOR) mcd123@mail.ustc.edu.cn
Source: International Journal for Numerical Methods in Engineering. May2026, Vol. 127 Issue 10, p1-25. 25p.
Subjects: Domain decomposition methods, Multigrid methods (Numerical analysis), Parallel algorithms, Numerical analysis, Parallel programming
Abstract: The multilevel Schwarz preconditioner, which integrates multigrid methods and Schwarz domain decomposition techniques, is one of the most popular parallel preconditioners for enhancing convergence and improving parallel efficiency. However, its design and parallel implementation on arbitrary unstructured triangular/tetrahedral meshes remain challenging. The challenges mainly arise from the inability to ensure that mesh hierarchies are nested, which complicates parallelization efforts. This article systematically investigates the non‐nested unstructured‐mesh case of parallel multilevel algorithms and develops a highly parallel non‐nested multilevel smoothed Schwarz preconditioner (NNMS). The proposed NNMS preconditioner incorporates two key techniques. The first is a new parallel coarsening algorithm that preserves the geometric features of the computational domain. The second is a corresponding parallel non‐nested interpolation method designed for non‐nested mesh hierarchies. This new preconditioner is applied to a broad range of linear parametric problems, benefiting from the reusability of the same coarse mesh hierarchy for problems with different parameters. Several numerical experiments validate the outstanding convergence and parallel efficiency of the NNMS preconditioner, demonstrating effective scalability up to 1000 processors. [ABSTRACT FROM AUTHOR]
Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell 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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  Data: <searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Multigrid+methods+%28Numerical+analysis%29%22">Multigrid methods (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel+algorithms%22">Parallel algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel+programming%22">Parallel programming</searchLink>
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  Data: The multilevel Schwarz preconditioner, which integrates multigrid methods and Schwarz domain decomposition techniques, is one of the most popular parallel preconditioners for enhancing convergence and improving parallel efficiency. However, its design and parallel implementation on arbitrary unstructured triangular/tetrahedral meshes remain challenging. The challenges mainly arise from the inability to ensure that mesh hierarchies are nested, which complicates parallelization efforts. This article systematically investigates the non‐nested unstructured‐mesh case of parallel multilevel algorithms and develops a highly parallel non‐nested multilevel smoothed Schwarz preconditioner (NNMS). The proposed NNMS preconditioner incorporates two key techniques. The first is a new parallel coarsening algorithm that preserves the geometric features of the computational domain. The second is a corresponding parallel non‐nested interpolation method designed for non‐nested mesh hierarchies. This new preconditioner is applied to a broad range of linear parametric problems, benefiting from the reusability of the same coarse mesh hierarchy for problems with different parameters. Several numerical experiments validate the outstanding convergence and parallel efficiency of the NNMS preconditioner, demonstrating effective scalability up to 1000 processors. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell 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: 10.1002/nme.70350
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      – Code: eng
        Text: English
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        PageCount: 25
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    Subjects:
      – SubjectFull: Domain decomposition methods
        Type: general
      – SubjectFull: Multigrid methods (Numerical analysis)
        Type: general
      – SubjectFull: Parallel algorithms
        Type: general
      – SubjectFull: Numerical analysis
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      – SubjectFull: Parallel programming
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      – TitleFull: A Non‐Nested Mesh Perspective on Highly Parallel Multilevel Schwarz Preconditioner.
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              M: 05
              Text: May2026
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              Y: 2026
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            – TitleFull: International Journal for Numerical Methods in Engineering
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