Development of Solvers for Systems of Linear Algebraic Equations for Cell-Centered Methods with a 7-Point Discretization Stencil.
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| Title: | Development of Solvers for Systems of Linear Algebraic Equations for Cell-Centered Methods with a 7-Point Discretization Stencil. |
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| Authors: | Puzikova, V. V.1 (AUTHOR) v.puzikova@yadro.com |
| Source: | Technical Physics. May2026, Vol. 71 Issue 5, p313-326. 14p. |
| Subjects: | Discretization methods, Domain decomposition methods, Algebraic equations, Hydrodynamics, Iterative methods (Mathematics), Algebraic multigrid methods |
| Abstract: | Solvers of systems of linear algebraic equations based on domain decomposition and multigrid methods demonstrate high efficiency in solving two-dimensional problems using cell-centered methods with a 5-point discretization stencil. In the 3D case, such methods utilize a 7-point stencil, requiring modification of the solvers. The aim of this work is to develop similar solvers for systems arising from the solution of three-dimensional problems using cell-centered methods with a 7-point discretization stencil. Formulas for computing the elements of the system matrices in three-dimensional subdomains and on interface planes, considering the 7-point stencil, are derived. It is shown that the structure of the interface system matrix coincides with the two-dimensional case. Therefore, the same direct solver used for 2D can be applied. Solving systems within subdomains is performed using the FGMRES method with preconditioning. When using the multigrid method as a preconditioner, certain parts of the algorithm require modifications for the transition from 2D to 3D. An algorithm for 3D ADLJ-smoother is presented. Since the considered system is derived from cell-centered grid methods where unknowns are located at cell centers rather than grid nodes, non-standard projection and prolongation operators are required for transferring between grid levels. The general principle for their constructing is demonstrated for 1D. Based on these formulas, three-dimensional operators are constructed for all possible cases. The developed solvers were verified on systems formed when solving three-dimensional hydrodynamics problems using the LS-STAG-3D immersed boundary cell-centered method with a 7-point stencil. For comparison, similar solvers for the two-dimensional case were also considered, applied to systems of the same dimension but formed from solving two-dimensional hydrodynamics problems using the LS-STAG method. Computational experiments show that the required accuracy is achieved in a comparable number of iterations for 2D and 3D problems of the same system dimension. [ABSTRACT FROM AUTHOR] |
| Copyright of Technical Physics is the property of Springer Nature 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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| Items | – Name: Title Label: Title Group: Ti Data: Development of Solvers for Systems of Linear Algebraic Equations for Cell-Centered Methods with a 7-Point Discretization Stencil. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Puzikova%2C+V%2E+V%2E%22">Puzikova, V. V.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> v.puzikova@yadro.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Technical+Physics%22">Technical Physics</searchLink>. May2026, Vol. 71 Issue 5, p313-326. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+equations%22">Algebraic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Hydrodynamics%22">Hydrodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+multigrid+methods%22">Algebraic multigrid methods</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Solvers of systems of linear algebraic equations based on domain decomposition and multigrid methods demonstrate high efficiency in solving two-dimensional problems using cell-centered methods with a 5-point discretization stencil. In the 3D case, such methods utilize a 7-point stencil, requiring modification of the solvers. The aim of this work is to develop similar solvers for systems arising from the solution of three-dimensional problems using cell-centered methods with a 7-point discretization stencil. Formulas for computing the elements of the system matrices in three-dimensional subdomains and on interface planes, considering the 7-point stencil, are derived. It is shown that the structure of the interface system matrix coincides with the two-dimensional case. Therefore, the same direct solver used for 2D can be applied. Solving systems within subdomains is performed using the FGMRES method with preconditioning. When using the multigrid method as a preconditioner, certain parts of the algorithm require modifications for the transition from 2D to 3D. An algorithm for 3D ADLJ-smoother is presented. Since the considered system is derived from cell-centered grid methods where unknowns are located at cell centers rather than grid nodes, non-standard projection and prolongation operators are required for transferring between grid levels. The general principle for their constructing is demonstrated for 1D. Based on these formulas, three-dimensional operators are constructed for all possible cases. The developed solvers were verified on systems formed when solving three-dimensional hydrodynamics problems using the LS-STAG-3D immersed boundary cell-centered method with a 7-point stencil. For comparison, similar solvers for the two-dimensional case were also considered, applied to systems of the same dimension but formed from solving two-dimensional hydrodynamics problems using the LS-STAG method. Computational experiments show that the required accuracy is achieved in a comparable number of iterations for 2D and 3D problems of the same system dimension. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Technical Physics is the property of Springer Nature 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1134/S1063784226700313 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 313 Subjects: – SubjectFull: Discretization methods Type: general – SubjectFull: Domain decomposition methods Type: general – SubjectFull: Algebraic equations Type: general – SubjectFull: Hydrodynamics Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Algebraic multigrid methods Type: general Titles: – TitleFull: Development of Solvers for Systems of Linear Algebraic Equations for Cell-Centered Methods with a 7-Point Discretization Stencil. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Puzikova, V. V. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10637842 Numbering: – Type: volume Value: 71 – Type: issue Value: 5 Titles: – TitleFull: Technical Physics Type: main |
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