volume | PIER Journals

Abstract

We propose a generalized hybrid method to achieve time efficient and accurate solutions for electromagnetic scattering and radiation problems involving complex scenes with multiple objects. The method utilizes frequency domain solutions, and is based on dividing the original computational domain into smaller sub-domains. Each sub-domain is first solved independently, then the interactions between the sub-domains are accounted for through an iterative procedure. The main difference of the proposed hybrid method in comparison with the current hybrid methods or the domain decomposition methods available in the literature is that the proposed method allows users to have the freedom to choose from a variety of techniques for each sub-domain; such as integral equation (IE), analytical and asymptotic methods that suit the problem at hand best. Current hybrid or domain decompositions methods rely on a predetermined combination of numerical techniques. This flexibility in the choice of the method employed for each sub-domain in the generalized hybrid method is achieved by creating an interface capable of interacting between the different sub-domains properly. Furthermore, the method renders to parallel implementation as each sub-domain is solved independently. The hybrid method in its current state can be applied to two different scenarios: (i) multiple non-touching homogeneous objects, and (ii) inhomogeneous objects. Numerical examples of various combinations of IE, analytical and asymptotic methods are presented to validate the accuracy and the robustness of the generalized hybrid method.

1. Harrington, R. F., Field Computation by Moment Method, Krieger Publ., Malabar, FL, 1982.

2. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Ant. Propag., Vol. 14, 302-307, 1966.
doi:10.1109/TAP.1966.1138693

3. Jin , J. M., The Finite Element Method in Electromagnetics, John Wiley & Sons, New York, 1993.

4. Volakis, J. L., A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications, IEEE Press, Piscataway, New Jersey, 1998.

5. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propagat. Mag., Vol. 35, No. 3, 7-12, Jun. 1993.
doi:10.1109/74.250128

6. Song, J. M. and W. C. Chew, "Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering," Microw. Opt. Tech. Lett., Vol. 10, 14-19, Sep. 1995.
doi:10.1002/mop.4650100107

7. Canning, F. X., "The impedance matrix localization (IML) method for moment-method calculations," IEEE Antennas Propagat. Mag., Vol. 32, No. 5, 18-30, 1990.
doi:10.1109/74.80583

8. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems," Radio Science, Vol. 31, No. 5, 1225-1251, 1996.
doi:10.1029/96RS02504

9. Stupfel, B. and M. Mognot, "A domain decomposition method for the vector wave equation," IEEE Trans. Antennas Propag., Vol. 48, No. 5, 653-660, May 2000.
doi:10.1109/8.855483

10. Li, Y.-J. and J.-M. Jin, "A new dual-primal domain decomposition approach for finite element simulation of 3-D large-scale electromagnetic problems," IEEE Trans. Antennas Propag., Vol. 55, No. 10, 2803-2810, Oct. 2007.
doi:10.1109/TAP.2007.905954

11. Lu, C. C. and W. C. Chew, "The use of Huygens’ equivalence principle for solving 3-D volume integral equation of scattering," IEEE Trans. Antennas Propag., Vol. 43, No. 5, 500-507, May 1995.
doi:10.1109/8.384194

12. Jensen, M. A. and J. D. Freeze, "A recursive Green’s function method for boundary integral analysis of inhomogeneous domains," IEEE Trans. Antennas Propag., Vol. 46, No. 12, 1810-1816, Dec. 1998.
doi:10.1109/8.743817

13. Xu, F. and W. Hong, "Analysis of two dimensions sparse multicylinder scattering problem using DD-FDTD method," IEEE Trans. Antennas Propagat., Vol. 52, No. 10, 2612-2617, Oct. 2004.
doi:10.1109/TAP.2004.834435

14. Monorchio, A., A. R. Bretones, R. Mittra, G. Manara, and R. G. Martin, "A hybrid time-domain technique that combines the finite element, finite difference and method of moment techniques to solve complex electromagnetic problems," IEEE Trans. Antennas Propagat., Vol. 52, 2666-2673, 2004.
doi:10.1109/TAP.2004.834431

15. Al Sharkawy, M. H., V. Demir, and A. Z. Elsherbeni, "The iterative multi-region algorithm using a hybrid finite difference frequency domain and method of moment techniques," Progress In Electromagnetics Research, Vol. 57, 19-32, 2006.
doi:10.2528/PIER05071001

16. Hodges, R. E. and Y. Rahmat-Samii, "An iterative current-based hybrid method for complex structures," IEEE Trans. Antennas Propagat., Vol. 45, No. 2, 265-276, 1997.
doi:10.1109/8.560345

17. Jakobus, U. and F. M. Landstorfer, "Improved PO-MM hybrid formulation for scattering from three-dimensional perfectly conducting bodies of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 43, No. 2, 162-169, 1995.
doi:10.1109/8.366378

18. Chen, M., X. W. Zhao, Y. Zhang, and C. H. Liang, "Analysis of antenna around NURBS surface with iterative MoM-PO technique," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 12, 1667-1680, 2006.
doi:10.1163/156939306779292372

19. Carr, M. and J. L. Volakis, "Domain decomposition by iterative field bouncing," IEEE AP-S International Symposium (Digest), Vol. 3, 298-301, San Antonio, TX, 2001.

20. Kim, C. S. and Y. Rahmat-Samii, "Low profile antenna study using the physical optics hybrid method (POHM)," Antennas and Propagation Society International Symposium, 1991, AP-S Digest, 1350-1353, IEEE, 1991.
doi:10.1109/APS.1991.175100

21. Nguyen, Q. and O. Kilic, "Electromagnetic scattering from multiple domains using a hybrid numerical and analytical solution," ACES 2014, Jacksonville, FL, USA, Mar. 23–27, 2014.

22. Nguyen, Q. and O. Kilic, "A hybrid method for electromagnetic scattering from multiple conducting objects," APS-URSI 2014, Memphis, TN, USA, Jul. 6–12, 2014.

23. Phan, T., Q. Nguyen, and O. Kilic, "A hybrid technique for electromagnetic scattering from threedimensional inhomogeneous dielectric objects," ACES 2016, Honolulu, Hawaii, Mar. 13–17, 2016.

24. Hansen, J. E., et al., Spherical Near-Field Antenna Measurements, Vol. 26, ser. IEE Electromagnetic Waves Series, Peter Peregrinus, London, UK, 1988.
doi:10.1049/PBEW026E

25. Devaney, A. J. and E. Wolf, "Multipole expansions and plane wave representations of the electromagnetic field," Journal of Mathematical Physics, Vol. 15, No. 2, 234-244, 1974.
doi:10.1063/1.1666629

26. Cappellin, C., O. Breinbjerg, and A. Frandsen, "Properties of the transformation from the spherical wave expansion to the plane wave expansion," Radio Sci., Vol. 43, No. 1, 2008.
doi:10.1029/2007RS003696

27. Atkinson, C. K., "Numerical integration on the sphere," J. Austral. Mat. Soc. B, Vol. 23, No. 3, 332-347, 1982.
doi:10.1017/S0334270000000278

28. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Tables, Dover, 1970.

29. Nguyen, Q. and O. Kilic, "An alternative plane wave decomposition of electromagnetic fields using the spherical wave expansion technique," IEEE Antennas and Wireless Propagation Letters, Vol. 16, 153-156, 2017.
doi:10.1109/LAWP.2016.2562182

Dr. Quang M. Nguyen

Dr. Ozlem Kilic