Efficient Parameter-Robust Preconditioners for Linear Poroelasticity and Elasticity in the Primal Formulation.
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| Title: | Efficient Parameter-Robust Preconditioners for Linear Poroelasticity and Elasticity in the Primal Formulation. |
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| Authors: | Huang, Weizhang1 (AUTHOR) whuang@ku.edu, Wang, Zhuoran1 (AUTHOR) wangzr@ku.edu |
| Source: | SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 3, pA1536-A1563. 28p. |
| Subjects: | Poroelasticity, Schur complement, Numerical analysis, Elasticity, Finite element method, Iterative methods (Mathematics), Krylov subspace |
| Abstract: | Poroelasticity problems play an important role in various engineering, geophysical, and biological applications. Their full discretization results in a large-scale saddle-point system at each time step that is becoming singular for locking cases and needs effective preconditioners for its fast iterative solution. Instead of constructing spectrally equivalent ones, we develop nonsingular preconditioners so that the eigenvalues of the preconditioned system consist of a cluster around 1 and an outlier in the order of \(1/\lambda\) , where \(\lambda\) is a Lamé constant that is large for locking cases. It is known that the convergence factor of GMRES is bounded by the radius of the cluster for this type of system. Both two- and three-field block triangular Schur complement preconditioners are studied. Upper bounds of the radius of the eigenvalue cluster for those systems are obtained and shown to be related to the inf-sup condition but independent of mesh size, time step, and the locking parameter \(\lambda\) , which reflects the robustness of the preconditioners with respect to parameter variations. Moreover, the developed preconditioners do not need to compute the Schur complement, and neither requires exact inversion of diagonal blocks except the leading one. A locking-free weak Galerkin finite element method and the implicit Euler scheme are used for the discretization of the governing equation. Both two- and three-dimensional numerical results are presented to confirm the effectiveness and parameter robustness of the developed preconditioners. [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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 195221988 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Efficient Parameter-Robust Preconditioners for Linear Poroelasticity and Elasticity in the Primal Formulation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Huang%2C+Weizhang%22">Huang, Weizhang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> whuang@ku.edu</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Zhuoran%22">Wang, Zhuoran</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wangzr@ku.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Scientific+Computing%22">SIAM Journal on Scientific Computing</searchLink>. 2026, Vol. 48 Issue 3, pA1536-A1563. 28p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Poroelasticity%22">Poroelasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Schur+complement%22">Schur complement</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Krylov+subspace%22">Krylov subspace</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Poroelasticity problems play an important role in various engineering, geophysical, and biological applications. Their full discretization results in a large-scale saddle-point system at each time step that is becoming singular for locking cases and needs effective preconditioners for its fast iterative solution. Instead of constructing spectrally equivalent ones, we develop nonsingular preconditioners so that the eigenvalues of the preconditioned system consist of a cluster around 1 and an outlier in the order of \(1/\lambda\) , where \(\lambda\) is a Lamé constant that is large for locking cases. It is known that the convergence factor of GMRES is bounded by the radius of the cluster for this type of system. Both two- and three-field block triangular Schur complement preconditioners are studied. Upper bounds of the radius of the eigenvalue cluster for those systems are obtained and shown to be related to the inf-sup condition but independent of mesh size, time step, and the locking parameter \(\lambda\) , which reflects the robustness of the preconditioners with respect to parameter variations. Moreover, the developed preconditioners do not need to compute the Schur complement, and neither requires exact inversion of diagonal blocks except the leading one. A locking-free weak Galerkin finite element method and the implicit Euler scheme are used for the discretization of the governing equation. Both two- and three-dimensional numerical results are presented to confirm the effectiveness and parameter robustness of the developed preconditioners. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/24M1672882 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: A1536 Subjects: – SubjectFull: Poroelasticity Type: general – SubjectFull: Schur complement Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Elasticity Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Krylov subspace Type: general Titles: – TitleFull: Efficient Parameter-Robust Preconditioners for Linear Poroelasticity and Elasticity in the Primal Formulation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Huang, Weizhang – PersonEntity: Name: NameFull: Wang, Zhuoran IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10648275 Numbering: – Type: volume Value: 48 – Type: issue Value: 3 Titles: – TitleFull: SIAM Journal on Scientific Computing Type: main |
| ResultId | 1 |
