Generalized Finite Difference Method for Solving Waveguide Eigenvalue Problems

Authors

  • Hui Xu Department of Electronic and Optics Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210000, China
  • Yang Bao 1)Department of Electronic and Optics Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210000, China 2) State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China

DOI:

https://doi.org/10.13052/2022.ACES.J.370302

Keywords:

Cutoff wavenumber, generalized finite difference method, meshless method, waveguide eigenvalue problem

Abstract

The generalized finite difference method (GFDM) is a meshless method that has become popular in recent years. The basic theory underlying GFDM is to expand the point cluster function value at the center node by Taylor’s formula and then obtain the best linear combinations of these function values to represent the derivative at the central node by the least square fitting technique. Subsequently, the minimized weighted error between the approximated value and the accurate value is obtained. This paper establishes the general steps for solving waveguide eigenvalue problems with GFDM. Excellent performance is shown by comparing the proposed method and other common solutions. The robustness of the proposed method is verified by calculating the cutoff wavenumbers of typical waveguides and the eccentric circular waveguide in different modes.

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Author Biographies

Hui Xu, Department of Electronic and Optics Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210000, China

Hui Xu was born in Wuxi, Jiangsu, China. He received the B.Eng. degree from the Nanjing University of Posts and Telecommunications, Nanjing, China. He is currently working toward the M.S. degree with the School of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications.

His research interests include the electromagnetic field theory, electromagnetic engineering, and computer aided analysis and design.

Yang Bao, 1)Department of Electronic and Optics Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210000, China 2) State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China

Yang Bao was born in Nanjing, Jiangsu, China. He received the B.Eng. and M.S. degrees from the Nanjing University of Posts and Telecommunications, Nanjing, China, in 2011 and 2014, respectively, and the Ph.D. degree in electrical engineering from Iowa State University, Ames, IA, USA, in 2019.

In December 2019, he joined the Nanjing University of Posts and Telecommunications as an Assistant Professor with the School of Electronic and Optical Engineering. His research interests focus on modeling and simulations of composite material, electromagnetic wave scattering using fast algorithms, and eddy current nondestructive evaluation.

References

J. R. Pyle, “The cutoff wavelength of the TE10 mode in ridged rectangular waveguide of any aspect ratio,” IEEE Trans. Microw. Theory and Techn., vol. 14, no. 4, pp. 175-183, Apr. 1966.

Y. J. Zhao, K. L. Wu, and K. Cheng, “A compact 2-D full-wave finite-difference frequency-domain method for general guided wave structures,” IEEE Trans. Microw. Theory and Techn., vol. 50, no. 7, pp. 1844-1848, Jul. 2002.

D. H. Chai, Harrington, and W. Hoefer, “The Finite-Difference-Time-Domain method and its application to eigenvalue problems,” IEEE Trans. Microw. Theory and Techn., vo. 34, no. 12, pp. 1464-1470, Dec. 1986.

J. Svedin, “Propagation analysis of chirowaveguides using the finite-element method,” IEEE Trans. Microw. Theory and Techn., vol. 38, no. 10, pp. 1488-1496, Oct. 1990.

J. A. Pereda and A. Grande, “Analysis of homogeneous waveguides via the meshless radial basis Function-Generated-Finite-Difference method,” IEEE Micro. and Wirel. Compon. Lett., vol. 30, no. 3, pp. 229-232, Mar. 2020.

V. Lombardi, M. Bozzi, and L. Perregrini, “Evaluation of the dispersion diagram of inhomogeneous waveguides by the variational meshless method,” IEEE Trans. Microw. Theory and Techn., vol. 67, no. 6, pp. 2105-2113, Jun. 2019.

S. Yang, Z. Chen, and Y. Yu, “A Divergence-Free meshless method based on the vector basis function for transient electromagnetic analysis,” IEEE Trans. Microw. Theory and Techn., vol. 62, no. 7, pp. 1409-1416, Jul. 2014.

L. Gavete, M. L. Gavete, and J. J. Benito, “Improvements of generalized finite difference method and comparison with other meshless method,” Appl. Math. Model., vol. 27, no. 10, pp. 831-847, Oct. 2003.

L. Gavete, F. Urena, and J. J. Benito, “Solving second order non-linear elliptic partial differential equations using generalized finite difference method,” J. Comput. Appl. Math., vol. 318,pp. 378-387, Jul. 2017.

J. J. Benito, and F. Urea, “An h-adaptive method in the generalized finite differences,” Comput. Meth. Appl. Mech. Eng., vol. 192, no. 5-6, pp. 735-759, Jan. 2003.

J. J. Benito, F. Urena, and L. Gavete, “Influence of several factors in the generalized finite difference method,” Appl. Math. Model., vol. 25, no. 12, pp. 1039-1053, Dec. 2001.

A. Kamyabi, V. Kermani, and M. Kamyabi, “Improvements to the meshless generalized finite difference method,” Eng. Anal. Bound. Elem., vol. 99, pp. 233-243, Feb. 2019.

P. W. Li and C. M. Fan, “Generalized finite difference method for two-dimensional shallow water equations,” Eng. Anal. Bound. Elem., vol. 80, pp. 58-71, Jul. 2017.

Y. Gu and L. Wang, “Application of the meshless generalized finite difference method to inverse heat source problems,” Int. J. Heat Mass Transf., vol. 108, pp. 721-729, May 2017.

T. Zhang, Y. F. Ren, C. M. Fan, and P. W. Li, “Simulation of two-dimensional sloshing phenomenon by generalized finite difference method,” Eng. Anal. Bound. Elem., vol. 63, pp. 82-91,Feb. 2016.

C. Jian, G. Yan, and M. Wang, “Application of the generalized finite difference method to three-dimensional transient electromagnetic problems,” Eng. Anal. Bound. Elem., vol. 92, pp. 257-266, Jul. 2017.

H. Xu, Y. C. Mei, and Y. Bao, “Application of generalized finite difference method in analysis of transmission characteristics of waveguide,” 2020 APMC., Hong Kong., China, pp. 785-787, 2020.

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Published

2022-03-31

How to Cite

[1]
H. . Xu and Y. . Bao, “Generalized Finite Difference Method for Solving Waveguide Eigenvalue Problems”, ACES Journal, vol. 37, no. 03, pp. 266–272, Mar. 2022.

Issue

2022: Vol 37 Iss 3

Section

General Submission

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