Preconditioning of a pollution-free discretization of the Helmholtz equation.
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| Title: | Preconditioning of a pollution-free discretization of the Helmholtz equation. |
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| Authors: | Monsuur, Harald1 (AUTHOR) harald.monsuur@hotmail.com |
| Source: | Applied Numerical Mathematics. Sep2026, Vol. 227, p169-187. 19p. |
| Subjects: | Helmholtz equation, Schur complement, Iterative methods (Mathematics), Optimization algorithms, Discretization methods, Least squares, Error analysis in mathematics |
| Abstract: | We present a pollution-free first order system least squares (FOSLS) formulation for the Helmholtz equation, solved iteratively using a block preconditioner. This preconditioner consists of two components: one for the Schur complement, which corresponds to a preconditioner on L 2 (Ω), and another defined on the test space, which we ensure remains Hermitian positive definite using subspace correction techniques. The proposed method is easy to implement and is directly applicable to general domains, including scattering problems. Numerical experiments demonstrate a linear dependence of the number of MINRES iterations on the wave number κ. We also introduce an approach to estimate algebraic errors which prevents unnecessary iterations. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Numerical Mathematics 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: 194123927 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Preconditioning of a pollution-free discretization of the Helmholtz equation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Monsuur%2C+Harald%22">Monsuur, Harald</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> harald.monsuur@hotmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Sep2026, Vol. 227, p169-187. 19p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Helmholtz+equation%22">Helmholtz equation</searchLink><br /><searchLink fieldCode="DE" term="%22Schur+complement%22">Schur complement</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Least+squares%22">Least squares</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We present a pollution-free first order system least squares (FOSLS) formulation for the Helmholtz equation, solved iteratively using a block preconditioner. This preconditioner consists of two components: one for the Schur complement, which corresponds to a preconditioner on L 2 (Ω), and another defined on the test space, which we ensure remains Hermitian positive definite using subspace correction techniques. The proposed method is easy to implement and is directly applicable to general domains, including scattering problems. Numerical experiments demonstrate a linear dependence of the number of MINRES iterations on the wave number κ. We also introduce an approach to estimate algebraic errors which prevents unnecessary iterations. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Numerical Mathematics 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.apnum.2026.04.012 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 169 Subjects: – SubjectFull: Helmholtz equation Type: general – SubjectFull: Schur complement Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Optimization algorithms Type: general – SubjectFull: Discretization methods Type: general – SubjectFull: Least squares Type: general – SubjectFull: Error analysis in mathematics Type: general Titles: – TitleFull: Preconditioning of a pollution-free discretization of the Helmholtz equation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Monsuur, Harald IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01689274 Numbering: – Type: volume Value: 227 Titles: – TitleFull: Applied Numerical Mathematics Type: main |
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