An overlapping domain decomposition method for parametric Stokes and Stokes-Darcy problems via proper generalized decomposition.
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| Title: | An overlapping domain decomposition method for parametric Stokes and Stokes-Darcy problems via proper generalized decomposition. |
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| Authors: | Discacciati, Marco1 (AUTHOR) m.discacciati@lboro.ac.uk, Evans, Ben J.1 (AUTHOR) b.j.evans@lboro.ac.uk, Giacomini, Matteo2,3 (AUTHOR) matteo.giacomini@upc.edu |
| Source: | Computer Methods in Applied Mechanics & Engineering. Jun2026, Vol. 455, pN.PAG-N.PAG. 1p. |
| Subjects: | Domain decomposition methods, Stokes equations, Reduced-order models, Optimization algorithms, Finite element method |
| Abstract: | A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality of the parametric flow fields and on an overlapping domain decomposition (DD) paradigm to reduce the number of globally coupled degrees of freedom in space. The DD-PGD approach provides a non-intrusive framework in which end-users only need access to the matrices arising from the (finite element) discretization of the full-order problems in the subdomains. The traces of the finite element functions used for the discretization within the subdomains are employed to impose arbitrary Dirichlet boundary conditions at the interface, without introducing auxiliary basis functions. The methodology is seamless to the choice of the discretization schemes in space, being compatible with both LBB-compliant finite element pairs and stabilized formulations, and the DD-PGD paradigm is transparent to the employed overlapping DD approach. The local surrogate models are glued together in the online phase by solving a parametric interface system to impose continuity of the subdomain solutions at the interfaces, without introducing Lagrange multipliers to enforce the continuity in the entire overlap and without solving any additional physical problem in the reduced space. Numerical results are presented for parametric single-physics (Stokes-Stokes) and multi-physics (Stokes-Darcy) systems, showcasing the accuracy, robustness, and computational efficiency of DD-PGD. [ABSTRACT FROM AUTHOR] |
| Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. 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: 192566869 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: An overlapping domain decomposition method for parametric Stokes and Stokes-Darcy problems via proper generalized decomposition. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Discacciati%2C+Marco%22">Discacciati, Marco</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> m.discacciati@lboro.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Evans%2C+Ben+J%2E%22">Evans, Ben J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> b.j.evans@lboro.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Giacomini%2C+Matteo%22">Giacomini, Matteo</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> matteo.giacomini@upc.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computer+Methods+in+Applied+Mechanics+%26+Engineering%22">Computer Methods in Applied Mechanics & Engineering</searchLink>. Jun2026, Vol. 455, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Stokes+equations%22">Stokes equations</searchLink><br /><searchLink fieldCode="DE" term="%22Reduced-order+models%22">Reduced-order models</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality of the parametric flow fields and on an overlapping domain decomposition (DD) paradigm to reduce the number of globally coupled degrees of freedom in space. The DD-PGD approach provides a non-intrusive framework in which end-users only need access to the matrices arising from the (finite element) discretization of the full-order problems in the subdomains. The traces of the finite element functions used for the discretization within the subdomains are employed to impose arbitrary Dirichlet boundary conditions at the interface, without introducing auxiliary basis functions. The methodology is seamless to the choice of the discretization schemes in space, being compatible with both LBB-compliant finite element pairs and stabilized formulations, and the DD-PGD paradigm is transparent to the employed overlapping DD approach. The local surrogate models are glued together in the online phase by solving a parametric interface system to impose continuity of the subdomain solutions at the interfaces, without introducing Lagrange multipliers to enforce the continuity in the entire overlap and without solving any additional physical problem in the reduced space. Numerical results are presented for parametric single-physics (Stokes-Stokes) and multi-physics (Stokes-Darcy) systems, showcasing the accuracy, robustness, and computational efficiency of DD-PGD. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. 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: 10.1016/j.cma.2026.118878 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Domain decomposition methods Type: general – SubjectFull: Stokes equations Type: general – SubjectFull: Reduced-order models Type: general – SubjectFull: Optimization algorithms Type: general – SubjectFull: Finite element method Type: general Titles: – TitleFull: An overlapping domain decomposition method for parametric Stokes and Stokes-Darcy problems via proper generalized decomposition. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Discacciati, Marco – PersonEntity: Name: NameFull: Evans, Ben J. – PersonEntity: Name: NameFull: Giacomini, Matteo IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00457825 Numbering: – Type: volume Value: 455 Titles: – TitleFull: Computer Methods in Applied Mechanics & Engineering Type: main |
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