On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections
This work addresses the suitability of using structured meshes composed of quadrilateral finite elements, instead of the classical unstructured meshes made of triangular elements. These meshes are used in the modal analysis of waveguides with Manhattan-like cross-sections. For this problem, solved w...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/4/656 |
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| author | Mohamad Hosein Rasekhmanesh Gines Garcia-Contreras Juan Córcoles Jorge A. Ruiz-Cruz |
| author_facet | Mohamad Hosein Rasekhmanesh Gines Garcia-Contreras Juan Córcoles Jorge A. Ruiz-Cruz |
| author_sort | Mohamad Hosein Rasekhmanesh |
| collection | DOAJ |
| description | This work addresses the suitability of using structured meshes composed of quadrilateral finite elements, instead of the classical unstructured meshes made of triangular elements. These meshes are used in the modal analysis of waveguides with Manhattan-like cross-sections. For this problem, solved with the two-dimensional Finite Element Method, there are two main quality metrics: eigenvalue and eigenvector accuracy. The eigenvalue accuracy is first considered, showing how the proposed structured meshes are, given comparable densities, better, especially when dealing with waveguides presenting pairs of modes with the same cutoff frequency. The second metric is measured through a practical problem, which commonly appears in microwave engineering: discontinuity analysis. In this problem, for which the Mode-Matching technique is used, eigenvectors are needed to compute the coupling between the modes in the discontinuities, directly influencing the quality of the transmission and reflection parameters. In this case, it is found that the proposed analysis performs better given low-density meshes and mode counts, thus proving that quadrilateral-element structured meshes are more resilient than their triangular counterparts to higher-order eigenvectors. |
| first_indexed | 2024-03-09T21:30:39Z |
| format | Article |
| id | doaj.art-947424b617d148ccbe467ffdfb906d5b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:30:39Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-947424b617d148ccbe467ffdfb906d5b2023-11-23T20:58:08ZengMDPI AGMathematics2227-73902022-02-0110465610.3390/math10040656On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-SectionsMohamad Hosein Rasekhmanesh0Gines Garcia-Contreras1Juan Córcoles2Jorge A. Ruiz-Cruz3Group of RadioFrequency: Circuits and Systems (RFCAS), Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainGroup of RadioFrequency: Circuits and Systems (RFCAS), Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainGroup of RadioFrequency: Circuits and Systems (RFCAS), Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainGroup of RadioFrequency: Circuits and Systems (RFCAS), Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, SpainThis work addresses the suitability of using structured meshes composed of quadrilateral finite elements, instead of the classical unstructured meshes made of triangular elements. These meshes are used in the modal analysis of waveguides with Manhattan-like cross-sections. For this problem, solved with the two-dimensional Finite Element Method, there are two main quality metrics: eigenvalue and eigenvector accuracy. The eigenvalue accuracy is first considered, showing how the proposed structured meshes are, given comparable densities, better, especially when dealing with waveguides presenting pairs of modes with the same cutoff frequency. The second metric is measured through a practical problem, which commonly appears in microwave engineering: discontinuity analysis. In this problem, for which the Mode-Matching technique is used, eigenvectors are needed to compute the coupling between the modes in the discontinuities, directly influencing the quality of the transmission and reflection parameters. In this case, it is found that the proposed analysis performs better given low-density meshes and mode counts, thus proving that quadrilateral-element structured meshes are more resilient than their triangular counterparts to higher-order eigenvectors.https://www.mdpi.com/2227-7390/10/4/656finite-element methodmode-matching methodLagrange elementstriangular cell typesquadrilateral cell typesdegenerate mode analysis |
| spellingShingle | Mohamad Hosein Rasekhmanesh Gines Garcia-Contreras Juan Córcoles Jorge A. Ruiz-Cruz On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections Mathematics finite-element method mode-matching method Lagrange elements triangular cell types quadrilateral cell types degenerate mode analysis |
| title | On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections |
| title_full | On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections |
| title_fullStr | On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections |
| title_full_unstemmed | On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections |
| title_short | On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections |
| title_sort | on the use of quadrilateral meshes for enhanced analysis of waveguide devices with manhattan type geometry cross sections |
| topic | finite-element method mode-matching method Lagrange elements triangular cell types quadrilateral cell types degenerate mode analysis |
| url | https://www.mdpi.com/2227-7390/10/4/656 |
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