volume | PIER Journals

Abstract

Numerical analysis of a generalized form of the recently developed electric and magnetic current combined field integral equation (JM-CFIE) for electromagnetic scattering by homogeneous dielectric and composite objects is presented. This new formulation contains a similar coupling parameter α as CFIE contains in the case of perfectly conducting objects. Two alternative JM-CFIE(α) formulations are introduced and their numerical properties (solution accuracy and convergence of iterative Krylov subspace methods) are investigated. The properties of these formulations are found to be very sensitive to the choice of α and to the permittivity of the object. By using normalized fields and currents the optimal value of α minimizing the number of iterations becomes only weakly dependent on the permittivity object. Using linear-linear basis functions instead of the more conventional constant-linear (RWG) basis functions the solution accuracy can be made less dependent on the choice of α.

1. Kolundzija, B. M. and A. R. Djordjevic, Electromagnetic Modeling of Composite Metallic and Dielectric Structures, Artech House, Boston, 2002.

2. Mautz, J. R. and R. F. Harrington, "H-field, E-field and combined-field solutions for conducting bodies of revolution," Arch. Elektr. Ubertragung., Vol. 32, 157-164, 1978.

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

4. 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.
doi:10.1080/02726349008908254

5. Sheng, X.-Q., J.-M. Jin, J. Song, W. C. Chew, and C.-C. Lu, "Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies," IEEE Trans. Antennas Propag., Vol. 46, No. 11, 1718-1726, Nov. 1998.
doi:10.1109/8.736628

6. Jung, B. H., T. K. Sarkar, and Y.-S. Chung, "A survey of various frequency domain integral equations for the analysis of scattering from three-dimensional dielectric objects," Progress In Electromagnetic Research, Vol. 36, 193-246, 2002.
doi:10.2528/PIER02021702

7. Yla-Oijala, P. and M. Taskinen, "Application of combined field integral equation for electromagnetic scattering by composite metallic and dielectric objects," IEEE Trans. Antennas Propag., Vol. 53, No. 3, 1168-1173, March 2005.
doi:10.1109/TAP.2004.842640

8. Jung, B. H. and T. K. Sarkar, "Analysis of scattering from arbitrarily shaped 3-D conducting/dielectric composite objects using a combined field integral equation," J. of Electromag. Waves and Applicat., Vol. 18, No. 6, 729-743, June 2004.
doi:10.1163/156939304323105826

9. Jung, B. H., T. K. Sarkar, and M. Salazar-Palma, "Combined field integral equation for the analysis of scattering from threedimensional conducting bodies coated with a dielectric material ," Microwave Opt. Technol. Lett., Vol. 40, No. 6, 511-516, March 2004.
doi:10.1002/mop.20019

11. Ergul, O. and L. Gurel, "Improving the accuracy of the magnetic field integral equation with the linear-linear basis functions," Radio Science, Vol. 41, RS4004, 2006.
doi:10.1029/2005RS003307

10. Song, J. M. and W. C. Chew, "Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering," Microw. Opt. Technol. Lett., Vol. 10, No. 1, 14-19, Sep. 1995.
doi:10.1002/mop.4650100107

11. Ergul, O. and L. Gurel, "Improving the accuracy of the magnetic field integral equation with the linear-linear basis functions," Radio Science, Vol. 41, RS4004, 2006.
doi:10.1029/2005RS003307

12. Yla-Oijala, P., M. Taskinen, and S. Jarvenpaa, "Analysis of surface integral equations in electromagnetic scattering and radiation problems," Engineering Analysis with Boundary Elements, Vol. 12, 196-209, 2008.
doi:10.1016/j.enganabound.2007.08.004

13. Yla-Oijala, P., M. Taskinen, and S. Jarvenpaa, "Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods," Radio Science, Vol. 40, No. 6, RS6002, Nov. 2005.
doi:10.1029/2004RS003169

14. Zhu, A., S. Gedney, and J. L. Visher, "A study of combined field formulations for material scattering for a locally corrected Nystrom discretization," IEEE Trans. Antennas Propag., Vol. 53, No. 12, 4111-4120, Dec. 2005.
doi:10.1109/TAP.2005.859918

15. Lloyd, T. W., J. M. Song, and M. Yang, "Numerical study of surface integral formulations for low-contrast objects ," IEEE Antennas and Wireless Propagation Letters, Vol. 4, 482-485, 2005.
doi:10.1109/LAWP.2005.862062

16. Yla-Oijala, P. and M. Taskinen, "Improving conditioning of the electromagnetic surface integral equations using normalized field quantities," IEEE Trans. Antennas Propag., Vol. 55, No. 1, 178-185, Jan. 2007.
doi:10.1109/TAP.2006.888418

17. Ergul, O. and L. Gurel, "Accurate solutions of scattering problems involving low-contrast dielectric objects with surface integral equations," Proceedings of the Second European Conference on Antennas and Propagation, EuCAP 2007, 390, Edinburg, Nov. 2007.

18. Ergul, O. and L. Gurel, "Fast and accurate solutions of scattering problems involving dielectric objects with moderate and low contrasts ," Proceedings of 2007 Computational Electromagnetics Workshop, CEM’07, 59-64, Izmir, Turkey, August 30–31, 2007.

19. Taskinen, M. and P. Yla-Oijala, "Current and charge integral equation formulation," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 58-67, Jan. 2006.
doi:10.1109/TAP.2005.861580

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

21. Trintinalia, L. C. and H. Ling, "First order triangular patch basis functions for electromagnetic scattering analysis," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 11, 1521-1537, 2001.
doi:10.1163/156939301X00085

Dr. Pasi Yla-Oijala