Eigenanalysis of Two-Dimensional Acoustic Cavities Using Transfinite Interpolation
This paper discusses the efficient extraction of eigenfrequencies in two-dimensional acoustic cavities using higher order finite elements, called “Coons-patch macroelements”. The acoustic pressure is approximated within the entire domain using the bivariate transfinite (Coons-Gordon) interpolation f...
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2009-12-01
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| Series: | Journal of Algorithms & Computational Technology |
| Online Access: | https://doi.org/10.1260/174830109789621383 |
| _version_ | 1819031497591488512 |
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| author | Christopher G. Provatidis |
| author_facet | Christopher G. Provatidis |
| author_sort | Christopher G. Provatidis |
| collection | DOAJ |
| description | This paper discusses the efficient extraction of eigenfrequencies in two-dimensional acoustic cavities using higher order finite elements, called “Coons-patch macroelements”. The acoustic pressure is approximated within the entire domain using the bivariate transfinite (Coons-Gordon) interpolation formula. Basically, the proposed macroelements constitute a generalization of the well-known Serendipity and Lagrangian type elements. The paper investigates the performance of the proposed methodology in several examples and definitely correlates the necessity of using internal nodes or domain decomposition with the percentage of open boundaries over the entire boundary as well as their relative position. It was found that for simple shapes, the entire acoustic cavity can be considered as a single quadrilateral patch, i.e. as one Coons-patch macroelement, while for complex shapes the cavity should be divided into a small number of subregions. |
| first_indexed | 2024-12-21T06:46:59Z |
| format | Article |
| id | doaj.art-107df0efa9cd4fb5875a89de10a7ac1d |
| institution | Directory Open Access Journal |
| issn | 1748-3018 1748-3026 |
| language | English |
| last_indexed | 2024-12-21T06:46:59Z |
| publishDate | 2009-12-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Algorithms & Computational Technology |
| spelling | doaj.art-107df0efa9cd4fb5875a89de10a7ac1d2022-12-21T19:12:35ZengSAGE PublishingJournal of Algorithms & Computational Technology1748-30181748-30262009-12-01310.1260/174830109789621383Eigenanalysis of Two-Dimensional Acoustic Cavities Using Transfinite InterpolationChristopher G. ProvatidisThis paper discusses the efficient extraction of eigenfrequencies in two-dimensional acoustic cavities using higher order finite elements, called “Coons-patch macroelements”. The acoustic pressure is approximated within the entire domain using the bivariate transfinite (Coons-Gordon) interpolation formula. Basically, the proposed macroelements constitute a generalization of the well-known Serendipity and Lagrangian type elements. The paper investigates the performance of the proposed methodology in several examples and definitely correlates the necessity of using internal nodes or domain decomposition with the percentage of open boundaries over the entire boundary as well as their relative position. It was found that for simple shapes, the entire acoustic cavity can be considered as a single quadrilateral patch, i.e. as one Coons-patch macroelement, while for complex shapes the cavity should be divided into a small number of subregions.https://doi.org/10.1260/174830109789621383 |
| spellingShingle | Christopher G. Provatidis Eigenanalysis of Two-Dimensional Acoustic Cavities Using Transfinite Interpolation Journal of Algorithms & Computational Technology |
| title | Eigenanalysis of Two-Dimensional Acoustic Cavities Using Transfinite Interpolation |
| title_full | Eigenanalysis of Two-Dimensional Acoustic Cavities Using Transfinite Interpolation |
| title_fullStr | Eigenanalysis of Two-Dimensional Acoustic Cavities Using Transfinite Interpolation |
| title_full_unstemmed | Eigenanalysis of Two-Dimensional Acoustic Cavities Using Transfinite Interpolation |
| title_short | Eigenanalysis of Two-Dimensional Acoustic Cavities Using Transfinite Interpolation |
| title_sort | eigenanalysis of two dimensional acoustic cavities using transfinite interpolation |
| url | https://doi.org/10.1260/174830109789621383 |
| work_keys_str_mv | AT christophergprovatidis eigenanalysisoftwodimensionalacousticcavitiesusingtransfiniteinterpolation |