Solving the problems of the conductivity of heterogeneous media by the method of the discrete Radon transform.
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| Title: | Solving the problems of the conductivity of heterogeneous media by the method of the discrete Radon transform. |
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| Authors: | Boukour, Mustapha1 (AUTHOR) boukour.mustapha@uae.ac.ma, Derraz, Mohammed Rida2 (AUTHOR), El Mamouni, Anass3 (AUTHOR), El Omri, Abderrahim4 (AUTHOR) |
| Source: | Mathematics & Mechanics of Solids. Jun2026, Vol. 31 Issue 6, p1189-1207. 19p. |
| Subjects: | Radon transforms, Asymptotic homogenization, Numerical analysis, Orthogonal decompositions, Inhomogeneous materials, Electric conductivity, Integral equations |
| Abstract: | In the framework of periodic homogenization, the Fast Fourier Transform (FFT) homogenization method allows one to formulate the linear conduction problem as an integral equation whose solution can be represented in Fourier space. In this work, we demonstrate that this solution can also be expressed in real space, with a precise geometrical interpretation. Our homogenization method builds upon a combination of the Discrete Radon Transform proposed by Gelfand, Gindikin, and Graev and a plane and anti-plane vector decomposition in some specific directions. This new combination enables us to efficiently decompose a vector field into two orthogonal subspaces (curl and divergence-free components). Based on this proposed approach, the conduction problem is reduced to an integral equation, where the local fields and subsequently the macroscopic behaviors are expressed as a real series expansion. We introduce an iterative scheme utilizing the finite Radon transform to solve the residual integral equation. In comparison to the FFT-based scheme developed by Moulinec and Suquet, our numerical experiments demonstrate that for certain specific microstructures, our method yields accurate results at significantly lower computational cost. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics & Mechanics of Solids is the property of Sage Publications Inc. 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: 193858390 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Solving the problems of the conductivity of heterogeneous media by the method of the discrete Radon transform. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Boukour%2C+Mustapha%22">Boukour, Mustapha</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> boukour.mustapha@uae.ac.ma</i><br /><searchLink fieldCode="AR" term="%22Derraz%2C+Mohammed+Rida%22">Derraz, Mohammed Rida</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22El+Mamouni%2C+Anass%22">El Mamouni, Anass</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22El+Omri%2C+Abderrahim%22">El Omri, Abderrahim</searchLink><relatesTo>4</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Mechanics+of+Solids%22">Mathematics & Mechanics of Solids</searchLink>. Jun2026, Vol. 31 Issue 6, p1189-1207. 19p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Radon+transforms%22">Radon transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+homogenization%22">Asymptotic homogenization</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+decompositions%22">Orthogonal decompositions</searchLink><br /><searchLink fieldCode="DE" term="%22Inhomogeneous+materials%22">Inhomogeneous materials</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+conductivity%22">Electric conductivity</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+equations%22">Integral equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the framework of periodic homogenization, the Fast Fourier Transform (FFT) homogenization method allows one to formulate the linear conduction problem as an integral equation whose solution can be represented in Fourier space. In this work, we demonstrate that this solution can also be expressed in real space, with a precise geometrical interpretation. Our homogenization method builds upon a combination of the Discrete Radon Transform proposed by Gelfand, Gindikin, and Graev and a plane and anti-plane vector decomposition in some specific directions. This new combination enables us to efficiently decompose a vector field into two orthogonal subspaces (curl and divergence-free components). Based on this proposed approach, the conduction problem is reduced to an integral equation, where the local fields and subsequently the macroscopic behaviors are expressed as a real series expansion. We introduce an iterative scheme utilizing the finite Radon transform to solve the residual integral equation. In comparison to the FFT-based scheme developed by Moulinec and Suquet, our numerical experiments demonstrate that for certain specific microstructures, our method yields accurate results at significantly lower computational cost. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics & Mechanics of Solids is the property of Sage Publications Inc. 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: 10.1177/10812865251336703 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 1189 Subjects: – SubjectFull: Radon transforms Type: general – SubjectFull: Asymptotic homogenization Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Orthogonal decompositions Type: general – SubjectFull: Inhomogeneous materials Type: general – SubjectFull: Electric conductivity Type: general – SubjectFull: Integral equations Type: general Titles: – TitleFull: Solving the problems of the conductivity of heterogeneous media by the method of the discrete Radon transform. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Boukour, Mustapha – PersonEntity: Name: NameFull: Derraz, Mohammed Rida – PersonEntity: Name: NameFull: El Mamouni, Anass – PersonEntity: Name: NameFull: El Omri, Abderrahim IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10812865 Numbering: – Type: volume Value: 31 – Type: issue Value: 6 Titles: – TitleFull: Mathematics & Mechanics of Solids Type: main |
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