FFT-based computation of homogenized interface parameters
The homogenization of microstructured interfaces requires solving specific problems posed on semi-infinite bands. To tackle these problems with existing FFT-based algorithms, a reformulation of these band problems into fully periodic cell problems, posed on bounded domains, is established. This is p...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2022-07-01
|
| Series: | Comptes Rendus. Mécanique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.119/ |
| _version_ | 1797651451786297344 |
|---|---|
| author | Cornaggia, Rémi Touboul, Marie Bellis, Cédric |
| author_facet | Cornaggia, Rémi Touboul, Marie Bellis, Cédric |
| author_sort | Cornaggia, Rémi |
| collection | DOAJ |
| description | The homogenization of microstructured interfaces requires solving specific problems posed on semi-infinite bands. To tackle these problems with existing FFT-based algorithms, a reformulation of these band problems into fully periodic cell problems, posed on bounded domains, is established. This is performed thanks to a Dirichlet-to-Neumann operator and a decomposition of the solution involving a boundary corrector, in a Fourier framework. A fixed-point algorithm and an example choice of corrector are proposed. Comparisons with other computational methods support this proposition. |
| first_indexed | 2024-03-11T16:14:57Z |
| format | Article |
| id | doaj.art-2cec924eeebe44d3b702b7eaaf4edebc |
| institution | Directory Open Access Journal |
| issn | 1873-7234 |
| language | English |
| last_indexed | 2024-03-11T16:14:57Z |
| publishDate | 2022-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj.art-2cec924eeebe44d3b702b7eaaf4edebc2023-10-24T14:20:57ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342022-07-01350G229730710.5802/crmeca.11910.5802/crmeca.119FFT-based computation of homogenized interface parametersCornaggia, Rémi0https://orcid.org/0000-0003-1410-9800Touboul, Marie1https://orcid.org/0000-0003-4052-0994Bellis, Cédric2https://orcid.org/0000-0002-2493-855XSorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond ∂’Alembert, F-75005 Paris, FranceSchool of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UKAix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, FranceThe homogenization of microstructured interfaces requires solving specific problems posed on semi-infinite bands. To tackle these problems with existing FFT-based algorithms, a reformulation of these band problems into fully periodic cell problems, posed on bounded domains, is established. This is performed thanks to a Dirichlet-to-Neumann operator and a decomposition of the solution involving a boundary corrector, in a Fourier framework. A fixed-point algorithm and an example choice of corrector are proposed. Comparisons with other computational methods support this proposition.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.119/FFT-based solversHomogenizationDirichlet-to-NeumannCell problemsBand problemsFFT-based solvers |
| spellingShingle | Cornaggia, Rémi Touboul, Marie Bellis, Cédric FFT-based computation of homogenized interface parameters Comptes Rendus. Mécanique FFT-based solvers Homogenization Dirichlet-to-Neumann Cell problems Band problems FFT-based solvers |
| title | FFT-based computation of homogenized interface parameters |
| title_full | FFT-based computation of homogenized interface parameters |
| title_fullStr | FFT-based computation of homogenized interface parameters |
| title_full_unstemmed | FFT-based computation of homogenized interface parameters |
| title_short | FFT-based computation of homogenized interface parameters |
| title_sort | fft based computation of homogenized interface parameters |
| topic | FFT-based solvers Homogenization Dirichlet-to-Neumann Cell problems Band problems FFT-based solvers |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.119/ |
| work_keys_str_mv | AT cornaggiaremi fftbasedcomputationofhomogenizedinterfaceparameters AT touboulmarie fftbasedcomputationofhomogenizedinterfaceparameters AT belliscedric fftbasedcomputationofhomogenizedinterfaceparameters |