volume | PIER Journals

Abstract

An original iterative method based on the conjugate gradient algorithm is developed in this paper to study electromagnetic scattering. The Generalized Equivalent Circuit (GEC) method is used to model the problem and then deduce an electromagnetic equation based on the impedance operator. For validation purposes, the developed method has been applied to various iris structures. Results computed using the new implementation of the conjugate gradient are similar to theoretical values. The field and current distribution are identical to the ones obtained with the moment method. Moreover, the memory resources required for storage are significantly reduced.

1. Tsang, L., J. A. Kong, and K. Ding, Scattering of Electromagnetic Waves: Theories and Applications, John Wiley and Sons, Canada, 2000.
doi:10.1002/0471224286

2. Fleming, A. H. J., "A finite element method for composite scatterers," Progress In Electromagnetic Research, Vol. 2, 69-112, 1990.

3. Harrington, R. F., Field Computation by Moment Methods, Macmillan, New York, 1968.

4. Harrington, R. F. and T. K. Sarkar, "Boundary elements and the method of moments," 5th Int. Conf. Boundary Elements, 31-40, Hiroshima, Japan, November 8-11, 1983.

5. Nocedal, J. and S. Wright, Numerical Optimization, Springer Series in Operations Research, Springer-Verlag, New York, 1999.

6. Sarkar, T. K., "The conjugate gradient method as applied to electromagnetic field problems," IEEE Antennas and Propagation Society Newsletter, August 1986.

7. Volakis, J. L. and K. Barkeshli, "Applications of the conjugate gradient FFT method to radiation and scattering," Progress In Electromagnetic Research, Vol. 5, 159-239, 1991.

8. Peterson, A. F., S. L. Ray, C. H. Chan, and R. Mittra, "Numerical implementation of the conjugate gradient method and the Cg-FFT for electromagnetic scattering," Progress In Electromagnetic Research, Vol. 5, 241-300, 1991.

9. Sarkar, T. K., E. Arvas, and S. M. Rao, "Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies," IEEE Trans. Antennas Propagat., Vol. 34, No. 5, 635-640, 1986.
doi:10.1109/TAP.1986.1143871

10. Peterson, A. F. and R. Mittra, "Convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering problems," IEEE Trans. Antennas Propagat., Vol. 34, 1447-1454, 1986.
doi:10.1109/TAP.1986.1143780

11. Barkeshli, K. and J. L. Volakis, "Improving the convergence rate of the conjugate gradient FFT using subdomain basis functions," IEEE Trans. Antennas Propagat., Vol. 37, No. 7, 893-900, 1989.
doi:10.1109/8.29384

12. Cwik, T. A. and R. Mittra, "Scattering from a periodic array of free-standing arbitrarily shaped perfectly conducting or resistive patches," IEEE Trans. Antennas Propagat., Vol. 35, 1226-1234, 1987.
doi:10.1109/TAP.1987.1143999

13. Baudrand, H., "Representation by equivalent circuit of the integrals methods in microwave passive elements," European Microwave Conference, Vol. 2, 1359-1364, Budapest, Hungary, September 10-13, 1990.

14. Aguili, T., "Modélisation des composantes SFH planaires par la méthode des circuits équivalents généralisés,", Thesis Manuscript, National Engineering School of Tunis, Tunisia, 2000.

15. Baudrand, H. and D. Bajon, "Equivalent circuit representation for integral formulations of electromagnetic problems," International Journal of Numerical Modelling-electronic Networks Devices and Fields, Vol. 15, 23-57, January-February 2002.

16. Aubert, H. and H. Baudrand, L'Electromagnétisme par les Schémas Equivalents,, Cepaduès Éditions, 2003.

17. Markuwitz, N., Waveguide Handbook, Wiley-Interscience, New York, 1986.

18. Collin, E. R., Foundations for Microwave Engineering, Donald G. Dudley, Series Editor, IEEE Press, 2001.
doi:10.1109/9780470544662

19. Baudrand, H., Introduction au Calcul des Eléments de Circuits Passifs en Hyperfréquence, Cepaduès Éditions, 2001.

Dr. Haifa Belhadj

Dr. Sonia Mili

Dr. Taoufik Aguili