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On improving the robustness and scalability of shared-memory AMG solvers for point-block problems.

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Title: On improving the robustness and scalability of shared-memory AMG solvers for point-block problems.
Authors: Konshin, Igor N.1,2,3 (AUTHOR), Terekhov, Kirill M.1 (AUTHOR) terekhov@inm.ras.ru
Source: Russian Journal of Numerical Analysis & Mathematical Modelling. Apr2026, Vol. 41 Issue 2, p119-149. 31p.
Subjects: Algebraic multigrid methods, Matrix multiplications, Interpolation, Benchmark problems (Computer science), Numerical analysis
Abstract: A number of modifications of the basic algorithms for constructing a multilevel structure to improve the performance of the algebraic multigrid method for both scalar and point-block systems are considered in this paper. We explore the basic operations of transposing and multiplying sparse matrices, as well as ways to select the maximum independent subset in the graph of strong connections, methods for constructing the prolongation operator, and approaches to aggressive coarsening that reduce the operation complexity of the method. It is shown that the construction of an extended prolongation operator can significantly increase the accuracy of the method, but at the cost of higher operator complexity and longer execution times. This disadvantage can be compensated either by filtering small weights from the prolongation operator, or by using aggressive coarsening. Several approaches to aggressive coarsening are considered. To confirm the conclusions, a number of numerical experiments were performed on a series of matrices from a publicly available collection for problems on progressively refined grids. The method applicability is evaluated on systems derived from adaptively generated grids. Some performance analisys of shared and hybrid memory is provided. [ABSTRACT FROM AUTHOR]
Copyright of Russian Journal of Numerical Analysis & Mathematical Modelling is the property of De Gruyter 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.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 193145661
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  Data: On improving the robustness and scalability of shared-memory AMG solvers for point-block problems.
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  Data: <searchLink fieldCode="AR" term="%22Konshin%2C+Igor+N%2E%22">Konshin, Igor N.</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Terekhov%2C+Kirill+M%2E%22">Terekhov, Kirill M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> terekhov@inm.ras.ru</i>
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  Data: <searchLink fieldCode="JN" term="%22Russian+Journal+of+Numerical+Analysis+%26+Mathematical+Modelling%22">Russian Journal of Numerical Analysis & Mathematical Modelling</searchLink>. Apr2026, Vol. 41 Issue 2, p119-149. 31p.
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  Data: <searchLink fieldCode="DE" term="%22Algebraic+multigrid+methods%22">Algebraic multigrid methods</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+multiplications%22">Matrix multiplications</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Benchmark+problems+%28Computer+science%29%22">Benchmark problems (Computer science)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: A number of modifications of the basic algorithms for constructing a multilevel structure to improve the performance of the algebraic multigrid method for both scalar and point-block systems are considered in this paper. We explore the basic operations of transposing and multiplying sparse matrices, as well as ways to select the maximum independent subset in the graph of strong connections, methods for constructing the prolongation operator, and approaches to aggressive coarsening that reduce the operation complexity of the method. It is shown that the construction of an extended prolongation operator can significantly increase the accuracy of the method, but at the cost of higher operator complexity and longer execution times. This disadvantage can be compensated either by filtering small weights from the prolongation operator, or by using aggressive coarsening. Several approaches to aggressive coarsening are considered. To confirm the conclusions, a number of numerical experiments were performed on a series of matrices from a publicly available collection for problems on progressively refined grids. The method applicability is evaluated on systems derived from adaptively generated grids. Some performance analisys of shared and hybrid memory is provided. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Russian Journal of Numerical Analysis & Mathematical Modelling is the property of De Gruyter 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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      – Type: doi
        Value: 10.1515/rnam-2026-0009
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 31
        StartPage: 119
    Subjects:
      – SubjectFull: Algebraic multigrid methods
        Type: general
      – SubjectFull: Matrix multiplications
        Type: general
      – SubjectFull: Interpolation
        Type: general
      – SubjectFull: Benchmark problems (Computer science)
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
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      – TitleFull: On improving the robustness and scalability of shared-memory AMG solvers for point-block problems.
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            NameFull: Konshin, Igor N.
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            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
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              Value: 41
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