Degeneracy-Discriminating Modal FEM Computation in Higher Order Rotationally Symmetric Waveguides

Garcia-Contreras, Gines; Córcoles, Juan; Ruiz‐Cruz, Jorge A.

doi:10.1109/tap.2021.3083790

Cited by 12 publications

(15 citation statements)

References 19 publications

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“…quadrilateral-element cells offer a higher rate of accuracy for Manhattan-type structures. This is especially critical in the case of cross-sections that exhibit a high amount of degenerate (presenting the same cutoff wavenumber) modes, since the use of a numerical method generally does not guarantee that the computed modes will yield that exact same eigenvalue (up to machine precision), unless certain boundary conditions are imposed in symmetry planes [24]. Secondly, to study how this enhanced accuracy in computing waveguide modes (thanks to the use of quadrilateral cells) translates to the analysis of actual devices, we address the MM simulation of waveguide bandpass filters where modes in their different cross-sections are computed with 2D-FEM.…”

Section: Introductionmentioning

confidence: 99%

On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections

2022

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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.

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Section: Introductionmentioning

confidence: 99%

On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections

2022

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“…This type of problems have been intensively studied by many researchers along the last two decades. [1][2][3][4][5][6][7][8] These approaches provide a huge potential to configure computer aided design (CAD) tools in conjunction with the last developments relative to pre and post processors, new and more powerful meshers and solvers, and the need of adding new higher-order basis functions to the formulations. It may worth to review these procedures, trying to increase its reliability and robustness.…”

Section: Introductionmentioning

confidence: 99%

“…They have been called 2.5 dimensional problems by the finite elements community due to the need to approximate the three components of the field, but the mesh of the discretized problem has a bi‐dimensional (2D) character. This type of problems have been intensively studied by many researchers along the last two decades 1–8 . These approaches provide a huge potential to configure computer aided design (CAD) tools in conjunction with the last developments relative to pre and post processors, new and more powerful meshers and solvers, and the need of adding new higher‐order basis functions to the formulations.…”

Section: Introductionmentioning

confidence: 99%

Robust numerical approximation of 2.5‐dimensional electromagnetic problems by using finite elements

Gil

2022

Int J RF Mic Comp-Aid Eng

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When a numerical method is used to analyze or design an electromagnetic structure, as the finite element method, the introduction of the behavior of some component of the electromagnetic field (when this is known) allows to project the physical problem onto a two-dimensional mesh, multiplying the capacity of the method to make efficient computer aided design of complex devices as they are demanded nowadays. Though this is an old issue, which has been focused one or two decades ago, the arrival of higher-order function basis and powerful tools of meshing and post processing makes interesting to review this important field within the computational electromagnetic area.

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“…For the waveguide eigenvalue problem, the cutoff wavenumber of a simple shape is determined as the eigenvalue root of the eigenmodes in [1]. The numerical technique is another effective method, such as the finite element methods (FEM) [2] and the integral equation methods [3]. However, these traditional mesh methods require the creation of meshes and are computationally complex.…”

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confidence: 99%

“…where C au is the auxiliary boundary, I n are unknown coefficients, G(r, r ) = − jH (2) 0 (kr)/4 is the fundamental solution of the twodimensional Helmholtz equation, r = |r − r |, and H (2) 0 (•) is the secondkind Hankel function of order zero.…”

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confidence: 99%

Cutoff wavenumber analysis of arbitrarily shaped waveguides using regularized method of fundamental solutions with excitation sources

Yan,

He,

Xiong

et al. 2023

Electronics Letters

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The method of fundamental solutions with excitation source (MFS‐ES) is a reliable method for determining the eigenvalues of a two‐dimensional hollow waveguide. However, the accuracy in MFS‐ES is extremely dependent on the choice of the auxiliary boundary. In this work, to avoid the problem, a regularized MFS‐ES (RMFS‐ES) is proposed. First, to overcome the shortcomings of MFS, a regularized method of fundamental Solutions (RMFS) is proposed by borrowing the ideas of singular boundary method (SBM) and single layer regularized meshless method (SRMM). Second, the expressions for the fundamental solutions at the singularities are given by utilizing the subtraction and adding‐back technique (SAB). Third, the excitation source method is introduced to overcome the problem that the RMFS may also have spurious frequencies. Finally, to improve the accuracy of RMFS‐ES in solving polygonal waveguide eigenvalue, a wedge scheme (WS) is given. Numerical results show that the meshless RMFS‐ES is a promising numerical method for waveguide eigenvalue problems.

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Degeneracy-Discriminating Modal FEM Computation in Higher Order Rotationally Symmetric Waveguides

Cited by 12 publications

References 19 publications

On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections

On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections

Robust numerical approximation of 2.5‐dimensional electromagnetic problems by using finite elements

Cutoff wavenumber analysis of arbitrarily shaped waveguides using regularized method of fundamental solutions with excitation sources

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