Vol. 82
Latest Volume
All Volumes
PIER 185 [2026] PIER 184 [2025] PIER 183 [2025] PIER 182 [2025] PIER 181 [2024] PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2008-03-26
The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides
By
Progress In Electromagnetics Research, Vol. 82, 203-226, 2008
Abstract
A new numerical technique is proposed for analyzing arbitrary shaped hollow waveguides. The method is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. The results of the numerical experiments justifying the method are presented. The method is validated by circular waveguide,rectangular waveguide an equilateral triangular waveguide. We apply the method for multi connected domains and for waveguides with boundary singularities like the Lshaped waveguide. Good agreements between the simulated and the published results have been obtained. The method does not generate spurious eigenfrequencies.
Citation
Sergiy Reutskiy, "The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides," Progress In Electromagnetics Research, Vol. 82, 203-226, 2008.
doi:10.2528/PIER08022701
References

1. Morse, P. M. and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, 1953.

2. Bulley, R. M., "Analysis of arbitrary shaped waveguide by polynomial approximation," IEEE Trans. Microwave Theory Tech., Vol. 18, No. 12, 1022-1028, Dec. 1970.
doi:10.1109/TMTT.1970.1127406        Google Scholar

3. Lin, W. K., L. W. Li, T. S. Yeo, and M. S. Leong, "Analysis of metallic waveguides of large class of cross sections using polynomial approximation and superquadric functions," IEEE Trans. Microwave Theory Tech., Vol. 49, No. 6, 1136-1239, June 2001.
doi:10.1109/22.925504        Google Scholar

4. Tomas, D. T., "Functional approximations for solving boundary value problems by computer," IEEE Trans. Microwave Theory Tech., Vol. 17, No. 8, 447-454, Aug. 1969.
doi:10.1109/TMTT.1969.1126995        Google Scholar

5. Swaminathan, M., Arvas, T. K. Sarkar, and A. R. Djordjevic, "Computation of cutoff wavenumbers of TE and TM modes in waveguides of arbitrary cross sections using a surface integral formulation," IEEE Trans. Microwave Theory Tech., Vol. 38, No. 2, 154-159, Feb. 1990.
doi:10.1109/22.46425        Google Scholar

6. Guan, J. M. and C. C. Su, "Analysis of metallic waveguides with rectangular boundaries by using the finite-difference method and the simultaneous iteration with the Chebyshev acceleration," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 2, 374-382, Feb. 1995.
doi:10.1109/22.348098        Google Scholar

7. Hernandez-Lopez, M. A. and M. Quintillan-Gonzalez, "A finite element method code to analyze waveguide dispersion," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 3, 397-408, 2007.
doi:10.1163/156939307779367396        Google Scholar

8. Yener, N., "Algebraic function approximation in eigenvalue problems of lossless metallic waveguides: Examples," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 6, 731-745, 2006.
doi:10.1163/156939306776143442        Google Scholar

9. Yener, N., "Advancement of algebraic function approximation in eigenvalue problems of lossless metallic waveguides to infinite dimensions," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 12, 1611-1628, 2006.
doi:10.1163/156939306779292363        Google Scholar

10. Khalaj-Amirhosseini, M., "Analysis of longitudinally inhomogeneous waveguides using Taylor’s series expansion," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 8, 1093-1100, 2006.
doi:10.1163/156939306776930286        Google Scholar

11. Khalaj-Amirhosseini, M., "Analysis of longitudinally inhomogeneous waveguides using the Fourier series expansion," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1299-1310, 2006.
doi:10.1163/156939306779276758        Google Scholar

12. Xiao, J.-K., W.-S. Ji, S. Zhang, and Y. Li, "A field theoretical method for analyzing microwave cavity with arbitrary crosssection," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 4, 435-446, 2006.
doi:10.1163/156939306776117054        Google Scholar

13. Mei, Z. L. and F. Y. Xu, "A simple, fast and accurate method for calculating cutoff wavelengths for the dominant mode in elliptical waveguide," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 3, 367-374, 2007.
doi:10.1163/156939307779367440        Google Scholar

14. Yung, E. K. N. and W. Lin, "Theory of Cassinian waveguides," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 10, 1323-1331, 2007.
doi:10.1163/156939307783239483        Google Scholar

15. Shu, C. and Y. T. Chew, "Application of multi-domain GDQ method to analysis of waveguides with rectangular boundaries," Progress In Electromagnetic Research, Vol. 21, 1-19, 1999.
doi:10.2528/PIER98052601        Google Scholar

16. Shu, C., W. X. Wu, and C. M. Wang, "Analysis of metallic waveguides using least square-based finite difference method," CMC: Computers, Materials & Continua, Vol. 2, 189-200, 2005.        Google Scholar

17. Ooi, B. L. and G. Zhao, "Element-free method for analysis of arbitrarily-shaped hollow conducting waveguides," IEE Proceedings --- Microwaves, Antennas and Propagation, Vol. 152, No. 1, 31-34, Feb. 2005.
doi:10.1049/ip-map:20045009        Google Scholar

18. Zhao, G., B. L. Ooi, Y. J. Fan, Y. Q. Zhang, I. Ang, and Y. Gao, "Application of conformal meshless RBF coupled with coordinate transformation for arbitrary waveguide analysis," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 1, 3-14, 2007.
doi:10.1121/1.403714        Google Scholar

19. Kondapalli, P. S. and D. J. Shippy, "Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions," Journal of the Acoustical Society of America, Vol. 91, No. 4, 1844-1854, 1992.
doi:10.1016/S0893-9659(01)00053-2        Google Scholar

20. Karageorghis, A., "The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation," Applied Math. Letters, Vol. 14, 837-842, 2001.        Google Scholar

21. Chen, J. T., J. H. Lin, S. R. Kuo, and S. W. Chyuan, "Boundary element analysis for the Helmholtz eigenvalues problems with a multiply connected domain," Proc. R. Soc. Lond. A, Vol. 457, 2521-2546, 2001.        Google Scholar

22. Chen, J. T., L. W. Liu, and H. K. Hong, "Spurious and true eigensolutions of Helmholtz BIEs and BEMs for a multiply connected problem," Proc. R. Soc. Lond. A, Vol. 459, 1897-1924, 2003.
doi:10.1006/jsvi.2002.5038        Google Scholar

23. Chen, J. T., M. H. Chang, K. H. Chen, S. R. Lin, and , "The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function," Journal of Sound and Vibration, Vol. 257, 667-711, 2002.
doi:10.1016/j.enganabound.2004.10.005        Google Scholar

24. Chen, J. T., L. Chen, and Y. T. Lee, "Eigensolutions of multiply connected membranes using the method of fundamental solutions," Engineering Analysis with Boundary Elements, Vol. 29, 166-174, 2005.
doi:10.1163/156939306779292174        Google Scholar

25. Bucci, O. M., G. D’Elia, and M. Santojanni, "A fast multipole approach to 2D scattering evaluation based on a non redundant implementation of the method of auxiliary sources," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1715-1723, 2006.
doi:10.2528/PIER04072101        Google Scholar

26. Anastassiu, H. T., "Error estimation of the method of auxiliary sources (MAS) for scattering from an impedance circular cylinder," Progress In Electromagnetics Research, Vol. 52, 109-128, 2005.
doi:10.1163/156939307783152920        Google Scholar

27. Liu, X., Z. Wang, and S. Lai, "Element-free Galerkin method in electromagnetic scattering field computation," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1915-1923, 2007.
doi:10.1163/156939307779378772        Google Scholar

28. Ooi, B. L. and G. Zhao, "Element-free method for the analysis of partially-filled dielectric waveguides," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 2, 189-198, 2007.
doi:10.1016/j.enganabound.2005.10.006        Google Scholar

29. Li, Z. C., T. T. Lu, H. Y. Hu, H. S. Tsai, and A. H. D. Cheng, "The Trefftz method for solving eigenvalue problems," Engineering Analysis with Boundary Elements, Vol. 30, 292-308, 2006.
doi:10.1016/j.enganabound.2005.08.011        Google Scholar

30. Reutskiy, S. Y., "The method of fundamental solutions for Helmholtz eigenvalue problems in simply and multiply connected domains," Engineering Analysis with Boundary Elements, Vol. 30, 150-159, 2006.        Google Scholar

31. Reutskiy, S. Y., "The method of fundamental solutions for eigenproblems with Laplace and biharmonic operators," CMC: Computers, Materials Continua, Vol. 2, 177-188, 2005.        Google Scholar

32. Reutskiy, S. Y., "The Method of External Sources (MES) for eigenvalue problems with Helmholtz equation," CMES: Computer Modeling in Engineering & Sciences, Vol. 12, 27-39, 2006.
doi:10.1016/j.enganabound.2007.04.003        Google Scholar

33. Reutskiy, S. Y., "The methods of external and internal excitation for problems of free vibrations of non-homogeneous membranes," Engineering Analysis with Boundary Elements, Vol. 31, 906-918, 2007.        Google Scholar

34. Reutskiy, S. Y., "The Method of External Excitation for problems of free vibrations of non-homogeneous Timoshenko beams," International Journal for Computational Methods in Engineering Science & Mechanics, Vol. 8, 10-21, 2007.
doi:10.1016/S0955-7997(02)00017-6        Google Scholar

35. Chen, W., "Symmetric boundary knot method," Engineering Analysis with Boundary Elements, Vol. 26, 489-494, 2002.
doi:10.1016/j.cma.2007.02.004        Google Scholar

36. Chen, J. T., C. T. Chen, P . Y. Chen, and I. L. Chen, "A semi-analytical approach for radiation and scattering problems with circular boundaries," Computer Methods in Applied Mechanics and Engineering, Vol. 196, 2751-2764, 2007.        Google Scholar

37. Alves, C. J. S. and P. R. S. Antunes, "The method of fundamental solutions applied to the calculation of eigenfrequencies and eigenmodes of 2D simply connected shapes," CMC: Computers, Materials & Continua, Vol. 2, 251-266, 2005.
doi:10.1137/0704008        Google Scholar

38. Fox, L., P. Henrici, and C. Molor, "Approximations and bounds for eigenvalues of elliptic operators," SIAM J. Numer. Anal., Vol. 4, 89-102, 1967.
doi:10.1137/S0036144503437336        Google Scholar

39. Betcke, T. and L. N. Trefethen, "Reviving the method of particular solutions," SIAM Review, Vol. 47, 469-491, 2005.        Google Scholar

40. Trefethen, L. N. and T. Betcke, "Computed eigenmodes of planar regions," AMS Contemporary Mathematics, Vol. 412, 297-314, 2006.        Google Scholar

41. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipescipes in C++, 2nd Ed., Cambridge University Press, 2002.
doi:10.1070/RM1967v022n02ABEH001210

42. Kupradze, V. D., "On approximate solution of problems in mathematical physics," Russian Math. Surveys, Vol. 22, 58-108, 1967.        Google Scholar

43. Vekua, I. N., New Methods for Solving Elliptic Equations, North-Holland, 1967.

44. Hafner, C., The Generalized Multipole Technique for Computational Electromagnetics, Artech House Books, 1990.