A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals
In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/26/1/2 |
| _version_ | 1797543091252494336 |
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| author | Zhuo-Jia Fu Lu-Feng Li De-Shun Yin Li-Li Yuan |
| author_facet | Zhuo-Jia Fu Lu-Feng Li De-Shun Yin Li-Li Yuan |
| author_sort | Zhuo-Jia Fu |
| collection | DOAJ |
| description | In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is obtained by satisfying the considered governing equation at interior nodes and boundary conditions at boundary nodes. As compared with finite element method (FEM) results and the analytical solutions, the efficiency and accuracy of the proposed localized collocation solver are verified under a benchmark example. Then, the proposed method is applied to 2D phononic crystals with various lattice forms and scatterer shapes, where the related band structures, transmission spectra, and displacement amplitude distributions are calculated as compared with the FEM. |
| first_indexed | 2024-03-10T13:39:46Z |
| format | Article |
| id | doaj.art-80aed2523f4a4f0d9ded404a64bf8b17 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T13:39:46Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-80aed2523f4a4f0d9ded404a64bf8b172023-11-21T03:08:19ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-12-01261210.3390/mca26010002A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic CrystalsZhuo-Jia Fu0Lu-Feng Li1De-Shun Yin2Li-Li Yuan3Center for Numerical Simulation Software in Engineering & Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaCenter for Numerical Simulation Software in Engineering & Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaCenter for Numerical Simulation Software in Engineering & Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaShenzhen Guoyi Park Construction Co., Ltd., Shenzhen 518000, ChinaIn this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is obtained by satisfying the considered governing equation at interior nodes and boundary conditions at boundary nodes. As compared with finite element method (FEM) results and the analytical solutions, the efficiency and accuracy of the proposed localized collocation solver are verified under a benchmark example. Then, the proposed method is applied to 2D phononic crystals with various lattice forms and scatterer shapes, where the related band structures, transmission spectra, and displacement amplitude distributions are calculated as compared with the FEM.https://www.mdpi.com/2297-8747/26/1/2collocationT-complete functionphononic crystalsband structurestransmission spectra |
| spellingShingle | Zhuo-Jia Fu Lu-Feng Li De-Shun Yin Li-Li Yuan A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals Mathematical and Computational Applications collocation T-complete function phononic crystals band structures transmission spectra |
| title | A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals |
| title_full | A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals |
| title_fullStr | A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals |
| title_full_unstemmed | A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals |
| title_short | A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals |
| title_sort | localized collocation solver based on t complete functions for anti plane transverse elastic wave propagation analysis in 2d phononic crystals |
| topic | collocation T-complete function phononic crystals band structures transmission spectra |
| url | https://www.mdpi.com/2297-8747/26/1/2 |
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