ULTRA-WEAK VARIATIONAL FORMULATION FOR HETEROGENEOUS MAXWELL PROBLEM IN THE CONTEXT OF HIGH PERFORMANCE COMPUTING.
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| Title: | ULTRA-WEAK VARIATIONAL FORMULATION FOR HETEROGENEOUS MAXWELL PROBLEM IN THE CONTEXT OF HIGH PERFORMANCE COMPUTING. |
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| Authors: | PERNET, SEBASTIEN1, SIRDEY, MARGOT2, TORDEUX, SEBASTIEN2 |
| Source: | ESAIM: Proceedings & Surveys. 2023, Vol. 75, p96-122. 27p. |
| Subjects: | High performance computing, Variational principles, Electromagnetism, Domain decomposition methods, Maxwell equations |
| Abstract: | Electromagnetic simulations on large domains require a huge memory consumption. Domain decomposition methods, based on Trefftz methods, could be an answer to this issue. In this paper, we associate to heterogeneous three-dimensional Maxwell equations one variational formulation which can be obtained either by upwind fluxes or Riemann traces. We associate to this variational formulation an iterative Trefftz Krylov solver. The poor conditioning due to the use of plane wave basis functions is bypassed thanks to a compression strategy. Moreover, the developed iterative solver is accelerated thanks to a left preconditioner. The considered numerical cases illustrate the performance of this basis reduction, which leads to the consideration of an industrial case of more than 750 millions of degrees of freedom. [ABSTRACT FROM AUTHOR] |
| Copyright of ESAIM: Proceedings & Surveys is the property of EDP 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. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: ULTRA-WEAK VARIATIONAL FORMULATION FOR HETEROGENEOUS MAXWELL PROBLEM IN THE CONTEXT OF HIGH PERFORMANCE COMPUTING. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22PERNET%2C+SEBASTIEN%22">PERNET, SEBASTIEN</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22SIRDEY%2C+MARGOT%22">SIRDEY, MARGOT</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22TORDEUX%2C+SEBASTIEN%22">TORDEUX, SEBASTIEN</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22ESAIM%3A+Proceedings+%26+Surveys%22">ESAIM: Proceedings & Surveys</searchLink>. 2023, Vol. 75, p96-122. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22High+performance+computing%22">High performance computing</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+principles%22">Variational principles</searchLink><br /><searchLink fieldCode="DE" term="%22Electromagnetism%22">Electromagnetism</searchLink><br /><searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Maxwell+equations%22">Maxwell equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Electromagnetic simulations on large domains require a huge memory consumption. Domain decomposition methods, based on Trefftz methods, could be an answer to this issue. In this paper, we associate to heterogeneous three-dimensional Maxwell equations one variational formulation which can be obtained either by upwind fluxes or Riemann traces. We associate to this variational formulation an iterative Trefftz Krylov solver. The poor conditioning due to the use of plane wave basis functions is bypassed thanks to a compression strategy. Moreover, the developed iterative solver is accelerated thanks to a left preconditioner. The considered numerical cases illustrate the performance of this basis reduction, which leads to the consideration of an industrial case of more than 750 millions of degrees of freedom. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of ESAIM: Proceedings & Surveys is the property of EDP 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: 10.1051/proc/202375096 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 96 Subjects: – SubjectFull: High performance computing Type: general – SubjectFull: Variational principles Type: general – SubjectFull: Electromagnetism Type: general – SubjectFull: Domain decomposition methods Type: general – SubjectFull: Maxwell equations Type: general Titles: – TitleFull: ULTRA-WEAK VARIATIONAL FORMULATION FOR HETEROGENEOUS MAXWELL PROBLEM IN THE CONTEXT OF HIGH PERFORMANCE COMPUTING. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: PERNET, SEBASTIEN – PersonEntity: Name: NameFull: SIRDEY, MARGOT – PersonEntity: Name: NameFull: TORDEUX, SEBASTIEN IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: 2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 22673059 Numbering: – Type: volume Value: 75 Titles: – TitleFull: ESAIM: Proceedings & Surveys Type: main |
| ResultId | 1 |
