volume | PIER Journals

Abstract

The surface integral equation method is applied for the electromagnetic analysis of general metallic and dielectric structures of arbitrary shape. The method is based on the EFIE-CFIE-PMCHWT integral equation formulation with Galerkins type discretization. The numerical implementation is divided into three independent steps: First, the electric and magnetic field integral equations are presented and discretized individually in each non-metallic subdomain with the RWG basis and testing functions. Next the linearly dependent and zero unknowns are removed from the discretized system by enforcing the electromagnetic boundary conditions on interfaces and at junctions. Finally, the extra equations are removed by applying the wanted integral equation formulation, and the reduced system is solved. The division into these three steps has two advantages. Firstly, it greatly simplifies the treatment of composite ob jects with multiple metallic and dielectric regions and junctions since the boundary conditions are separated from the discretization and integral equation formulation. In particular, no special junction basis functions or special testing procedures at junctions are needed. Secondly, the separation of the integral equation formulation from the two previous steps makes it easy to modify the procedure for other formulations. The method is validated by numerical examples.

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

2. Medgyesi-Mitschang, L. N. and J. M. Putnam, "Electromagnetic scattering from axially inhomogeneous bodies of revolution," IEEE Trans. on Antennas and Propagation, Vol. 32, No. 8, 797-806, 1984.
doi:10.1109/TAP.1984.1143430

3. Govind, S., D. R. Wilton, and A. W. Glisson, "Scattering from inhomogeneous penetrable bodies of revolution," IEEE Trans. on Antennas and Propagation, Vol. 32, No. 11, 1163-1173, 1984.
doi:10.1109/TAP.1984.1143240

4. Huddleston, P. L., L. N. Medgyesi-Mitschang, and J. M. Putnam, "Combined field integral equation formulation for scattering by dielectrically coated conducting bodies," IEEE Trans. on Antennas and Propagation, Vol. 34, No. 4, 510-520, 1986.
doi:10.1109/TAP.1986.1143846

5. Putnam, J. M. and L. N. Medgyesi-Mitschang, "Combined field integral equation for inhomogeneous two-and three-dimensional bodies: The junction problem," IEEE Trans. Antennas and Propagation, Vol. 39, No. 5, 667-672, 1991.
doi:10.1109/8.81498

6. Goggans, P. M., A. A. Kishk, and A. W. Glisson, "Electromagnetic scattering from ob jects composed of multiple homogeneous regions using a region-by-region solution," IEEE Trans. Antennas and Propagation, Vol. 42, No. 6, 865-871, 1994.
doi:10.1109/8.301713

7. Ylä-Oijala, P. and E. Somersalo, "Computation of electromagnetic fields in axisymmetric RF structures with boundary integral equations," Journal of Electromagnetic Waves and Applications, Vol. 13, 445-489, 1999.

8. Sarkar, T. K., S. M. Rao, and A. R. Djordjevic, "Electromagnetic scattering and radiation from finite microstrip structures," IEEE Trans. on Microwave Theory and Techniques, Vol. 38, No. 11, 1568-1575, 1990.
doi:10.1109/22.60001

9. Rao, S. M., C. C. Cha, R. L. Cravey, and D. Wilkes, "Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness," IEEE Trans. on Antennas and Propagation, Vol. 39, No. 5, 627-631, 1991.
doi:10.1109/8.81490

10. Medgyesi-Mitschang, L. N., J. M. Putnam, and M. B. Gedera, "Generalized method of moments for three-dimensional penetrable scatterers," J. Opt. Soc. Am. A, Vol. 11, No. 4, 1383-1398, 1994.

11. Chen, Q. and D. R. Wilton, "Electromagnetic scattering by three-dimensional arbitrary complex material/conducting bodies," IEEE AP-S Symposium 1990, Vol. 2, 590-593, 1990.

12. Arvas, E., A. Rahhal-Arabi, A. Sadigh, and S. M. Rao, "Scattering from multiple conducting and dielectric bodies of arbitrary shape," IEEE Antennas and Propagation Magazine, Vol. 33, No. 2, 29-36, 1991.
doi:10.1109/74.88184

13. Shin, J., A. W. Glisson, and A. A. Kishk, "Analysis of combined conducting and dielectric structures of arbitrary shapes using an E-PMCHW integral equation formulation," IEEE AP-S Symposium 2000, Vol. 4, 2282-2285, 2000.

14. Donepudi, K. C., J.-M. Jin, and W. C. Chew, "A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies," IEEE Trans. Antennas and Propagation, Vol. 51, No. 10, 2814-2821, 2003.
doi:10.1109/TAP.2003.817979

15. Kolundzija, B. M., "Electromagnetic modelling of composite metallic and dielectric structures," IEEE Trans. on Microwave Theory and Techniques, Vol. 47, No. 7, 1021-1032, 1999.
doi:10.1109/22.775434

16. Shin, J., A. W. Glisson, and A. A. Kishk, "Modeling of general surface junctions of composite objects in an SIE/MoM formulation," 2000 ACES Conference Proceedings, 683-690, 2000.

17. Chew, W. C., J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001.

18. Carr, M., E. Topsakal, and J. L. Volakis, "A procedure for modeling material junctions in 3-D surface integral equation approaches," IEEE Trans. on Antennas and Propagation, Vol. 52, No. 5, 1374-1379, 2004.
doi:10.1109/TAP.2004.827247

19. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas and Propagation, Vol. AP-30, No. 3, 409-418, 1982.
doi:10.1109/TAP.1982.1142818

20. Mautz, J. R. and R. F. Harrington, "Electromagnetic scattering from a homogeneous material body of revolution," Arch. Elektron. Übertragungstechn. (Electron. Commun.), Vol. 33, 71-80, 1979.

21. Mautz, J. R. and R. F. Harrington, "H-field, E-field and combined-field solutions for conducting bodies of revolution," Arch. Elektron. Übertragungstechn. (Electron. Commun.), Vol. 32, 157-164, 1978.

22. Kress, R., Linear Integral Equations, Springer-Verlag, 1989.

23. Colton, D. and R. Kress, Integral Equation Methods in Scattering Theory, John Wiley & Sons, 1983.

24. Ylä-Oijala, P. and M. Taskinen, "Calculation of CFIE impedance matrix elements with RWG and n Ã— RWG functions," IEEE Trans. Antennas and Propagation, Vol. 51, No. 8, 1837-1846, 2003.
doi:10.1109/TAP.2003.814745

25. Rao, S. M. and D. R. Wilton, "E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies," Electromagnetics, Vol. 10, 407-421, 1990.

26. Umashankar, K., A. Taflove, and S. A. Rao, "Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects," IEEE Trans. Antennas and Propagation, Vol. AP-34, No. 6, 758-766, 1986.
doi:10.1109/TAP.1986.1143894

27. Pang, Y.-H. and R-B. Wu, "Analysis of microstrip antennas with finite-sized substrate," IEEE APS Symposium, Vol. 2, 814-817, 2001.

28. Chen, W., K.-F. Lee, and R. Q. Lee, "Input impedance of coaxially fed rectangular microstrip antenna on electrically thick substrate," Microwave and Optical Technology Letters, Vol. 6, No. 6, 387-390, 1993.

29. Ylä-Oijala, P., M. Taskinen, and J. Sarvas, "Multilayered media Green's functions for MPIE with general electric and magnetic sources by the Hertz potential approach," Progress in Electromagnetic Research, Vol. 33, 141-165, 2001.

30. Ylä-Oijala, P. and M. Taskinen, "Efficient formulation of closed form Green's functions for general electric and magnetic sources in multilayered media," IEEE Trans. Antennas and Propagation, Vol. 51, No. 8, 2106-2115, 2003.
doi:10.1109/TAP.2003.814738

31. Junker, G. P., A. A. Kishk, and A. W. Glisson, "Input impedance of dielectric resonator antennas excited by a coaxial probe," IEEE Trans. on Antennas and Propagation, Vol. 42, No. 7, 960-966, 1994.
doi:10.1109/8.299598

Dr. Pasi Yla-Oijala

Dr. Matti Taskinen

Dr. Jukka Sarvas