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.

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Published

2022-07-10

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, Jul. 2022.

Issue

2022: Vol 37 Iss 3

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