An efficient homogenization method using the trigonometric interpolation and the fast fourier transform
This study focuses on formulation of the Augmented Lagrangian and application of the Uzawa's algorithm to solve the homogenization problem of microscopic periodic media as in composites. Unlike in the finite element model, an equally spaced grid system associated with the microstructure domain...
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| Format: | Article |
| Language: | English |
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Publishing House for Science and Technology
2011-12-01
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| Series: | Vietnam Journal of Mechanics |
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| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/255 |
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| _version_ | 1850204602123681792 |
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| author | Ngoc-Trung Nguyen Christian Licht Jin-Hwe Kweon |
| author_facet | Ngoc-Trung Nguyen Christian Licht Jin-Hwe Kweon |
| author_sort | Ngoc-Trung Nguyen |
| collection | DOAJ |
| description |
This study focuses on formulation of the Augmented Lagrangian and application of the Uzawa's algorithm to solve the homogenization problem of microscopic periodic media as in composites. Unlike in the finite element model, an equally spaced grid system associated with the microstructure domain is used instead of a finite element mesh topology. Moreover, the trigonometric interpolations for the field variables at every grid point help to handle the periodic conditions. The proposed approach is a compromise between Lagrange multiplier and penalty methods, in that it enables exact representation of constraints while using penalty terms to facilitate the iteration procedure. A typical homogenization problem will be solved using this approach. The results show good consistency with those in literatures. Effects of the grid density and the penalty parameter on the convergence have also been investigated.
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| format | Article |
| id | doaj-art-733d0002b82b467e8303b682c3cb8e5d |
| institution | OA Journals |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2011-12-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-733d0002b82b467e8303b682c3cb8e5d2025-08-20T02:11:15ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822011-12-0133410.15625/0866-7136/33/4/255An efficient homogenization method using the trigonometric interpolation and the fast fourier transformNgoc-Trung Nguyen0Christian Licht1Jin-Hwe Kweon2Kangwon National University, Chunchon, Kangwon-doLMGC, Universit\'{e} de Montp\'{e}llier 2School of Mechanical and Aerospace Engineering, Gyeongsang National University This study focuses on formulation of the Augmented Lagrangian and application of the Uzawa's algorithm to solve the homogenization problem of microscopic periodic media as in composites. Unlike in the finite element model, an equally spaced grid system associated with the microstructure domain is used instead of a finite element mesh topology. Moreover, the trigonometric interpolations for the field variables at every grid point help to handle the periodic conditions. The proposed approach is a compromise between Lagrange multiplier and penalty methods, in that it enables exact representation of constraints while using penalty terms to facilitate the iteration procedure. A typical homogenization problem will be solved using this approach. The results show good consistency with those in literatures. Effects of the grid density and the penalty parameter on the convergence have also been investigated. https://vjs.ac.vn/index.php/vjmech/article/view/255Homogenizationaugmented Lagrangian methodtrigonometric interpolation |
| spellingShingle | Ngoc-Trung Nguyen Christian Licht Jin-Hwe Kweon An efficient homogenization method using the trigonometric interpolation and the fast fourier transform Vietnam Journal of Mechanics Homogenization augmented Lagrangian method trigonometric interpolation |
| title | An efficient homogenization method using the trigonometric interpolation and the fast fourier transform |
| title_full | An efficient homogenization method using the trigonometric interpolation and the fast fourier transform |
| title_fullStr | An efficient homogenization method using the trigonometric interpolation and the fast fourier transform |
| title_full_unstemmed | An efficient homogenization method using the trigonometric interpolation and the fast fourier transform |
| title_short | An efficient homogenization method using the trigonometric interpolation and the fast fourier transform |
| title_sort | efficient homogenization method using the trigonometric interpolation and the fast fourier transform |
| topic | Homogenization augmented Lagrangian method trigonometric interpolation |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/255 |
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