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AN ALGEBRAIC MULTIGRID METHOD FOR OSEEN PROBLEMS.

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Title: AN ALGEBRAIC MULTIGRID METHOD FOR OSEEN PROBLEMS.
Authors: NOTAY, YVAN1 yvan.notay@ulb.be
Source: SIAM Journal on Scientific Computing. 2025, Vol. 47 Issue 5, pA2506-A2532. 27p.
Subjects: Algebraic multigrid methods, Multigrid methods (Numerical analysis), Incompressible flow, Numerical analysis, Numerical solutions to equations, Convective flow, Iterative methods (Mathematics)
Abstract: We consider the numerical solution of discrete Oseen problems. We focus on the recently proposed transform-then-solve approach, which amounts to first applying a specific algebraic transformation to the linear system of equations arising from the discretization and then solving the transformed system with an algebraic multigrid method. Promising results have been previously obtained with a two-grid variant, and here we bring two key improvements to make the approach robust in a multilevel setting. For a model problem with a constant convection field, it is shown, in a local Fourier analysis setting, that the two-grid method is convergent at any level of the hierarchy, with bounds that are independent of both the mesh size and the Reynolds number. Numerical results with a K-cycle multigrid scheme confirm the theoretical expectations for constant coefficient problems. For problems with variable convective flow, the method appears also robust with grid independence convergence, although a mild dependency with respect to the Reynolds number shows up at very low viscosity in driven cavity problems. The method is based on point coarsening and therefore, besides the system matrix, requires knowing, for each discrete unknown, which grid point it is associated with. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics 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="%22Algebraic+multigrid+methods%22">Algebraic multigrid methods</searchLink><br /><searchLink fieldCode="DE" term="%22Multigrid+methods+%28Numerical+analysis%29%22">Multigrid methods (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Incompressible+flow%22">Incompressible flow</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+equations%22">Numerical solutions to equations</searchLink><br /><searchLink fieldCode="DE" term="%22Convective+flow%22">Convective flow</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink>
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  Data: We consider the numerical solution of discrete Oseen problems. We focus on the recently proposed transform-then-solve approach, which amounts to first applying a specific algebraic transformation to the linear system of equations arising from the discretization and then solving the transformed system with an algebraic multigrid method. Promising results have been previously obtained with a two-grid variant, and here we bring two key improvements to make the approach robust in a multilevel setting. For a model problem with a constant convection field, it is shown, in a local Fourier analysis setting, that the two-grid method is convergent at any level of the hierarchy, with bounds that are independent of both the mesh size and the Reynolds number. Numerical results with a K-cycle multigrid scheme confirm the theoretical expectations for constant coefficient problems. For problems with variable convective flow, the method appears also robust with grid independence convergence, although a mild dependency with respect to the Reynolds number shows up at very low viscosity in driven cavity problems. The method is based on point coarsening and therefore, besides the system matrix, requires knowing, for each discrete unknown, which grid point it is associated with. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics 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: 10.1137/24M1704488
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      – Code: eng
        Text: English
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        PageCount: 27
        StartPage: A2506
    Subjects:
      – SubjectFull: Algebraic multigrid methods
        Type: general
      – SubjectFull: Multigrid methods (Numerical analysis)
        Type: general
      – SubjectFull: Incompressible flow
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Numerical solutions to equations
        Type: general
      – SubjectFull: Convective flow
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
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      – TitleFull: AN ALGEBRAIC MULTIGRID METHOD FOR OSEEN PROBLEMS.
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            – D: 01
              M: 09
              Text: 2025
              Type: published
              Y: 2025
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