Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media
Sab et al. (2024) have recently proposed an FFT-based iterative algorithm, termed Adaptive Eyre–Milton (AEM), for solving the Lippmann–Schwinger equation in the context of periodic homogenization of infinitely double contrasted linear elastic composites (heterogeneous materials with linear constitut...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.269/ |
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| author | Dolbeau, Martin Bleyer, Jérémy Sab, Karam |
| author_facet | Dolbeau, Martin Bleyer, Jérémy Sab, Karam |
| author_sort | Dolbeau, Martin |
| collection | DOAJ |
| description | Sab et al. (2024) have recently proposed an FFT-based iterative algorithm, termed Adaptive Eyre–Milton (AEM), for solving the Lippmann–Schwinger equation in the context of periodic homogenization of infinitely double contrasted linear elastic composites (heterogeneous materials with linear constitutive laws that contain both pores and rigid inclusions). They have demonstrated the unconditional linear convergence of this scheme, regardless of initialization and the chosen reference material. However, numerical simulations have shown that the rate of convergence of AEM strongly depends on the chosen reference material. In this paper, we introduce a new version of the AEM scheme where the reference material is updated iteratively, resulting in a fast and versatile scheme, termed Accelerated Adaptive Eyre–Milton (A2EM). Numerical simulations with A2EM on linear elastic composites with both pores and infinitely rigid inclusions show that, regardless of the initial chosen reference material, this algorithm has the same rate of convergence as AEM with the best choice of reference material. |
| format | Article |
| id | doaj-art-9e79db6789d04b55913978baa4f1fcd1 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-9e79db6789d04b55913978baa4f1fcd12025-02-07T13:48:46ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342024-11-01352G125126710.5802/crmeca.26910.5802/crmeca.269Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted mediaDolbeau, Martin0Bleyer, Jérémy1Sab, Karam2Laboratoire Navier, IPParis ENPC, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, FranceLaboratoire Navier, Ecole Nationale des Ponts et Chaussées, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, FranceLaboratoire Navier, Ecole Nationale des Ponts et Chaussées, Univ Gustave Eiffel, CNRS, Marne-la-Vallée, FranceSab et al. (2024) have recently proposed an FFT-based iterative algorithm, termed Adaptive Eyre–Milton (AEM), for solving the Lippmann–Schwinger equation in the context of periodic homogenization of infinitely double contrasted linear elastic composites (heterogeneous materials with linear constitutive laws that contain both pores and rigid inclusions). They have demonstrated the unconditional linear convergence of this scheme, regardless of initialization and the chosen reference material. However, numerical simulations have shown that the rate of convergence of AEM strongly depends on the chosen reference material. In this paper, we introduce a new version of the AEM scheme where the reference material is updated iteratively, resulting in a fast and versatile scheme, termed Accelerated Adaptive Eyre–Milton (A2EM). Numerical simulations with A2EM on linear elastic composites with both pores and infinitely rigid inclusions show that, regardless of the initial chosen reference material, this algorithm has the same rate of convergence as AEM with the best choice of reference material.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.269/computational homogenizationFFT-based methoditerative schemelinear elasticitycomposite materials |
| spellingShingle | Dolbeau, Martin Bleyer, Jérémy Sab, Karam Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media Comptes Rendus. Mécanique computational homogenization FFT-based method iterative scheme linear elasticity composite materials |
| title | Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media |
| title_full | Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media |
| title_fullStr | Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media |
| title_full_unstemmed | Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media |
| title_short | Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media |
| title_sort | accelerating the adaptive eyre milton fft based method for infinitely double contrasted media |
| topic | computational homogenization FFT-based method iterative scheme linear elasticity composite materials |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.269/ |
| work_keys_str_mv | AT dolbeaumartin acceleratingtheadaptiveeyremiltonfftbasedmethodforinfinitelydoublecontrastedmedia AT bleyerjeremy acceleratingtheadaptiveeyremiltonfftbasedmethodforinfinitelydoublecontrastedmedia AT sabkaram acceleratingtheadaptiveeyremiltonfftbasedmethodforinfinitelydoublecontrastedmedia |