Academic Journal
Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots.
| Τίτλος: | Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots. |
|---|---|
| Συγγραφείς: | Bonizzoni, Francesca, Pradovera, Davide, Ruggeri, Michele |
| Πηγή: | Mathematics in Engineering; 2023, Vol. 5 Issue 4, p1-38, 38p |
| Θεματικοί όροι: | Boundary value problems, Approximation theory, Helmholtz equation, Finite element method, Mathematical formulas |
| Περίληψη: | We introduce several spatially adaptive model order reduction approaches tailored to noncoercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite elements, so that each snapshot lives in a different discrete space that resolves the local singularities of the analytical solution and is adjusted to the considered frequency value. A rational surrogate is then assembled adopting either a least-squares or an interpolatory approach, yielding a function-valued version of the the standard rational interpolation method (V-SRI) and the minimal rational interpolation method (MRI). In the context of building an approximation for linear or quadratic functionals of the Helmholtz solution, we perform several numerical experiments to compare the proposed methodologies. Our simulations show that, for interior resonant problems (whose singularities are encoded by poles on the real axis), the spatially adaptive V-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, the V-SRI method seems to be the best-performing one. [ABSTRACT FROM AUTHOR] |
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| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:edb&genre=article&issn=26403501&ISBN=&volume=5&issue=4&date=20230701&spage=1&pages=1-38&title=Mathematics in Engineering&atitle=Rational-approximation-based%20model%20order%20reduction%20of%20Helmholtz%20frequency%20response%20problems%20with%20adaptive%20finite%20element%20snapshots.&aulast=Bonizzoni%2C%20Francesca&id=DOI:10.3934/mine.2023074 Name: Full Text Finder (for New FTF UI) (ns324271) Category: fullText Text: Full Text Finder MouseOverText: Full Text Finder |
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| Items | – Name: Title Label: Title Group: Ti Data: Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bonizzoni%2C+Francesca%22">Bonizzoni, Francesca</searchLink><br /><searchLink fieldCode="AR" term="%22Pradovera%2C+Davide%22">Pradovera, Davide</searchLink><br /><searchLink fieldCode="AR" term="%22Ruggeri%2C+Michele%22">Ruggeri, Michele</searchLink> – Name: TitleSource Label: Source Group: Src Data: Mathematics in Engineering; 2023, Vol. 5 Issue 4, p1-38, 38p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Helmholtz+equation%22">Helmholtz equation</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+formulas%22">Mathematical formulas</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We introduce several spatially adaptive model order reduction approaches tailored to noncoercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite elements, so that each snapshot lives in a different discrete space that resolves the local singularities of the analytical solution and is adjusted to the considered frequency value. A rational surrogate is then assembled adopting either a least-squares or an interpolatory approach, yielding a function-valued version of the the standard rational interpolation method (V-SRI) and the minimal rational interpolation method (MRI). In the context of building an approximation for linear or quadratic functionals of the Helmholtz solution, we perform several numerical experiments to compare the proposed methodologies. Our simulations show that, for interior resonant problems (whose singularities are encoded by poles on the real axis), the spatially adaptive V-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, the V-SRI method seems to be the best-performing one. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Mathematics in Engineering is the property of American Institute of Mathematical Sciences 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: 10.3934/mine.2023074 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 38 StartPage: 1 Subjects: – SubjectFull: Boundary value problems Type: general – SubjectFull: Approximation theory Type: general – SubjectFull: Helmholtz equation Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Mathematical formulas Type: general Titles: – TitleFull: Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bonizzoni, Francesca – PersonEntity: Name: NameFull: Pradovera, Davide – PersonEntity: Name: NameFull: Ruggeri, Michele IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: 2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 26403501 Numbering: – Type: volume Value: 5 – Type: issue Value: 4 Titles: – TitleFull: Mathematics in Engineering Type: main |
| ResultId | 1 |