volume | PIER Journals

Abstract

Approximate, non-singular kernels are often used in moment-method formulations coping with thin-wire structures. Their use has important consequences, one of which is the appearance of oscillations in the computed currents when the number of sub-domain basis functions is sufficiently large. These oscillations are not due to round-off errors. In this paper, a smoothing procedure is used in conjunction with Galerkin's formulation with piecewise sinusoidal functions, which yields non-oscillating current distributions. Special attention is paid to the solutions over a wide range of discretization levels (number of basis/testing functions), in order to examine and illustrate the similarities and differences between results obtained with and without the proposed remedy. Finally, a comparison with results derived with the exact kernel is provided.

1. Harrington, R. F., Field Computation by Moment Methods, MacMillan, 1968.

2. Fikioris, G. and T. T. Wu, "On the application of numerical methods to Hallen's equation," IEEE Transactions on Antennas and Propagation, Vol. 49, No. 3, 383-392, 2001.
doi:10.1109/8.918612

3. Fikioris, G., "The approximate integral equation for a cylindrical scatterer has no solution," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 9, 1153-1159, 2001.

4. Fikioris, G., J. Lionas, and C. G. Lioutas, "The use of the frill generator in thin-wire integral equations," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 8, 1847-1854, 2003.
doi:10.1109/TAP.2003.815412

5. King, R. W. P., G. J. Fikioris, and R. B. Mack, Cylindrical Antennas and Arrays, Chs. 1 and 13, 2002.

6. Hallen, E., "Theoretical investigations into transmitting and receiving antennae," Nova Acta Regiae Societatis Scientiarum Upsaliensis IV, Vol. 11, 1-44, 1938.

7. Infeld, L., "The influence of the width of the gap upon the theory of antennas," Quarterly of Applied Mathematics, Vol. V, No. 2, 113-132, 1947.

8. King, R. W. P., "The linear antenna-eighty years of progress," Proceedings of the IEEE, Vol. 55, No. 1, 2-16, 1967.

9. Strait, B. J. and A. T. Adams, "On contributions at Syracuse University to the moment method," IEEE Transactions on Electromagnetic Compatibility, Vol. 22, No. 4, 228-237, 1980.
doi:10.1109/TEMC.1980.303860

10. Taylor, C. D. and D. R. Wilton, "The extended boundary condition solution of the dipole antenna of revolution," IEEE Transactions on Antennas and Propagation, Vol. 20, No. 6, 772-776, 1972.
doi:10.1109/TAP.1972.1140316

11. Miller, E. K. and F. J. Deadrick, "Some computational aspects of thin-wire modeling," Numerical and Asymptotic Techniques in Electromagnetics, 1975.

12. Burke, G. J., "The Numerical Electromagnetics Code (NEC)," Application of the Method of Moments to Electromagnetic Fields, 1980.

13. Poggio, A. J. and E. K. Miller, "Techniques for low-frequency problems," Antenna Handbook, Vol. I: Antenna Fundamentals and Mathematical Techniques, 1993.

14. Bancroft, R., Understanding Electromagnetic Scattering Using the Moment Method: A Practical Approach, Ch. 3, 1996.

15. Imbriale, W. A. and P. G. Ingerson, "On numerical convergence of moment solutions of moderately thick wire antennas using sinusoidal basis functions," IEEE Transactions on Antennas and Propagation, Vol. 21, No. 3, 363-366, 1973.
doi:10.1109/TAP.1973.1140478

16. Klein, C. A. and R. Mittra, "The effect of different testing functions in the moment method solution of thin-wire antenna formulations," IEEE Transactions on Antennas and Propagation, Vol. 23, No. 2, 258-261, 1975.
doi:10.1109/TAP.1975.1141033

17. Butler, C. M. and D. R. Wilton, "Analysis of various numerical techniques applied to thin-wire scatterers," IEEE Transactions on Antennas and Propagation, Vol. 23, No. 4, 534-540, 1975.
doi:10.1109/TAP.1975.1141108

18. Sarkar, T. K., "A study of the various methods for computing electromagnetic field utilizing thin wire integral equations," Radio Science, Vol. 18, No. 1, 29-38, 1983.

19. Sarkar, T. K., "A note on the choice weighting functions in the method of moments," IEEE Transactions on Antennas and Propagation, Vol. 33, No. 4, 436-441, 1985.
doi:10.1109/TAP.1985.1143590

20. Sarkar, T. K., A. R. Djordjevic, and E. Arvas, "On the choice of expansion and weighting functions in the numerical solution of operator equations," IEEE Transactions on Antennas and Propagatation, Vol. 33, No. 9, 988-996, 1985.
doi:10.1109/TAP.1985.1143707

21. Peterson, A. F., "Difficulties encountered when attempting to validate thin-wire formulations for linear dipole antennas," Applied Computational Electromagnetics Society Journal, Vol. 4, No. 3, 25-40, 1989.

22. Schelkunoff, S. A., Advanced Antenna Theory, Section 5.5, 1952.

23. Wu, T. T., "Introduction to linear antennas," Antenna Theory, 1969.

24. Fikioris, G. and C. A. Valagiannopoulos, "Input admittances arising from explicit solutions to integral equations for infinitelength dipole antennas," Progress In Electromagnetics Research, Vol. 55, 285-306, 2005.
doi:10.2528/PIER05031701

25. Papakanellos, P. J. and C. N. Capsalis, "On the combination of the method of auxiliary sources with reaction matching for the analysis of thin cylindrical antennas," International Journal of Numerical Modeling, Vol. 17, No. 5, 433-449, 2004.
doi:10.1002/jnm.549

26. Papakanellos, P. J., I. I. Heretakis, P. K. Varlamos, and C. N. Capsalis, "A combined method of auxiliary sources-reaction matching approach for analyzing moderately large-scale arrays of cylindrical dipoles," Progress In Electromagnetics Research, Vol. 59, 51-67, 2006.
doi:10.2528/PIER05091501

27. Fikioris, G., "On two types of convergence in the method of auxiliary sources," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 7, 2022-2033, 2006.
doi:10.1109/TAP.2006.877171

28. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, Ch. 4, 1992.

29. Wu, D., N. Inagaki, and N. Kikuma, "Hallen-type integral equation for cylindrical antennas with finite gap excitation," IEICE Transactions on Communications, Vol. E-82B, No. 12, 2145-2152, 1999.

30. Quesada-Pereira, F. D., J. L. GÂ´omez-Tornero, D. CaËœnete- Rebenaque, J. Pascual-García, and A. Â´Alvarez-MelcÂ´on, "Analysis of thick-wire antennas using a novel and simple kernel treatment," Microwave and Optical Technology Letters, Vol. 46, No. 4, 410-417, 2005.
doi:10.1002/mop.21002

Dr. Panagiotis Papakanellos

Professor George Fikioris