Numerical computation of cut off wave number in polygonal wave guide by eight node finite element mesh generation approach

Authors

  • K. T. Shivaram Department of Mathematics, Dayananda Sagar College of Engineering, Visvesvaraya Technological University, Bengaluru, India.
  • A. M. Yogitha Department of Mathematics, Dayananda Sagar College of Engineering, Visvesvaraya Technological University, Bengaluru, India.
  • S. M. Rajesh Department of Mechanical Engineering, Dayananda Sagar College of Engineering, Bangalore, India.
  • N. Mahesh Kumar Department of Electronics and Communication Engineering, Dayananda Sagar College of Engineering, Bangalore, India.

Abstract

This study proposes a two-dimensional, eight-noded automated mesh generator for precise and efficient finite element analysis (FEA) in microwave applications. The suggested method for solving the Helmholtz problem employs an optimal domain discretization procedure. MAPLE-13 software's advanced automatic mesh generator was developed specifically for this work. To demonstrate the effectiveness of the approach, three distinct waveguide structures are analyzed, with the results compared to the best available analytical or numerical solutions. The findings indicate that the proposed method yields highly accurate and efficient finite element results, particularly for waveguide structures containing singularities. In microwave applications, this method can significantly enhance energy transmission efficiency.

Dimensions

F. A. Fernandez & Y. Lu, Microwave and optical waveguide analysis by the finite element method, John Wiley & Sons, Inc.605 Third Ave. New York, NY, United States, 1996. https://dl.acm.org/doi/book/10.5555/547580.

T. Bernabeu-Jimenez, A. Valero-Nogueira, F. Vico-Bondia & A. A. Kishk, “A comparison be-tween natural resonances and characteristic mode resonances of an infinite circular cylinder”, IEEE Trans. Antennas Propag. 65 (2017) 5. https://ieeexplore.ieee.org/document/7856968.

D. Ramaccia1, M. Barbuto, A. Tobia1, F. Bilotti1 & A. Toscano1, “Efficient energy transfer through a bifilar metamaterial line connecting microwave waveguides”, J. Appl. Phys. 121 (2017) 054901. http://dx.doi.org/10.1063/1.4974957.

J. P. Montgomery, “On the complete eigenvalue solution of ridged waveguide”, IEEE Transactions on Microwave Theory and Techniques 19 (1971) 547. https://ieeexplore.ieee.org/document/1127572.

Y. H. Cho & H. J. Eom, “Fourier transform analysis of a ridge waveguide and a rectangular coaxial line”, Journal of Radio Sci. 36 (2001) 533. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000RS002381.

C.Y. Wang, “Determination of TM and TE modes of the circular wave guide with a cross-shaped insert using eigen function expansions and domain matching”, Journal of Electromagnetic Waves and Applications 30 (2016) 10. https://www.tandfonline.com/doi/full/10.1080/09205071.2016.1199331.

M. Kouroublakis, G. P. Zouros & N. L. Tsitsas, “An auxiliary-current vector norm method for computing the cutoff wave numbers of anisotropic waveguides” , IEEE Trans. Microwave Theory Tech. 71 (2023) 11. https://ieeexplore.ieee.org/document/10148653.

Y. H. Cho & H. J. Eom, “Analysis of a ridge waveguide using overlapping T-blocks”, IEEE Trans. Mi-crowave Theory Tech. 50 (2002) 2368. https://ieeexplore.ieee.org/document/1038877.

M. Swaminathan, E. Arvas, T. K. Sarkar & A. R. Djordjevic, “Computation of cutoff wave-numbers of TE and TM modes in waveguides of arbitrary cross sections using a surface integral formulation”, IEEE Trans. Microwave Theory Tech. 38 (1990) 154. https://ieeexplore.ieee.org/document/60030.

T. Sarkar, Y. Chung & M. Palma, “Solution of the general Helmholtz equation starting from Laplace’s equation”, Applied Computational Electromagnetics Society Journal 17 (2002) 3. https://apps.dtic.mil/sti/tr/pdf/ADP013470.pdf.

T. Yan, D. He, X. Xiong, S. Hu & B. Hu, “Cutoff wavenumber analysis of arbitrarily shaped waveguides using regularized method of fundamental solutions with excitation sources”, Electronic Letters 59 (2023) 4. https://doi.org/10.1049/ell2.13049.

K. Wang, J. J. Laurin, Q. Zhang, X. Ruan, Y. Li, Q. Zhang & K. Wu, “Cutoff wavenumber analyses of metallic waveguides filled with homogeneous anisotropic materials using the MFCM”, IEEE Trans. Microwave Theory Tech. 70 (2022) 5. https://doi.org/10.1109/tmtt.2022.3156968.

H. Xu & Y. Bao, “Generalized finite difference method for solving waveguide eigenvalue problems” Appl. Comput. Electromagn. Soci. J. 37 (2022) 3. https://doi.org/10.13052/2022.ACES.J.370302.

K. T. Shivaram, L. M. P. Harshitha, H. P. Chethana & K. Nidhi, “Finite element mesh generation technique for numerical computation of cutoff wave numbers in rectangular and L-shaped wave-guide”, 3rd International Conference on Inventive Computation Technologies (ICICT), IEEE Xplore (2018) 704. https://ieeexplore.ieee.org/abstract/document/9034432.

G. Strang & G. J. Fix, “An analysis of finite element method”, Prentice-Hall, Englwood Cliffs, NJ, 1973. https://archive.org/details/analysisoffinite0000stra/page/n7/mode/2up.

J. N. Reddy, An introduction to the finite element method, 3rd ed., Tata McGraw-Hill, 2005. https://www.accessengineeringlibrary.com/content/ book/9780072466850.

R. B. Sensale, B. Sensalea & V. Leitaob, “Determination of the TE and TM modes in arbitrarily shaped waveguides using a hypersingular boundary element formulation”, Int. J. Electron. Commun. 62 (2008) 576. https://doi.org/10.1016/j.aeue.2007.07.011.

S. Chang, Differential quadrature and its application in engineering, Springer Science and Business Media, London 2012. https://link.springer.com/book/10.1007/978-1-4471-0407-0.

K.T.Shivaram, “Generalised gaussian quadrature rules over an arbitrary tetrahedron in euclidean three-dimensional space”, International Journal of Applied Engineering Research 8 (2013) 1533. https://www. ripublication.com/ijaerv6/ijaerv8n1303.pdf.

M. Helen & V. Prabhakar, “Computational investigation of free convection flow inside inclined square cavities”, Journal of Nigerian Society of Physical Sciences 4 (2022) 2. https://journal.nsps.org.ng/index.php/jnsps/ article/view/637/146.

K. T. Shivaram, N. Mahesh Kumar, M. V. Goudar & S. Gagandeep, “A new Approach for evaluation of volume integrals by Haar wavelet method”, International Journal of Innovative Technology and Exploring Engineering 8 (2019) 2262 https://www.ijitee.org/portfolio-item/ H7153068819/

K. T. Shivaram & H. R. Jyothi, “Finite element approach for numerical integration over family of eight node linear quadrilateral element for solving Laplace equation”, Materials Today Proceedings 46 (2021) 4336. https://doi.org/10.1016/j.matpr.2021.03.437.

Published

2024-10-22

How to Cite

Numerical computation of cut off wave number in polygonal wave guide by eight node finite element mesh generation approach. (2024). Journal of the Nigerian Society of Physical Sciences, 6(4), 2149. https://doi.org/10.46481/jnsps.2024.2149

Issue

Volume 6, Issue 4, November 2024

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2024 K.T. Shivaram, A. M. Yogitha, S. M. Rajesh, N. Mahesh Kumar

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Numerical computation of cut off wave number in polygonal wave guide by eight node finite element mesh generation approach. (2024). Journal of the Nigerian Society of Physical Sciences, 6(4), 2149. https://doi.org/10.46481/jnsps.2024.2149