A general domain decomposition scheme based on the use of complex sources is presented for the electromagnetic analysis of complex antenna and/or scattering problems. The analysis domain is decomposed into separate subdomains whose interactions are described through a network formalism, where the ports are associated with complex point source (CPS) beams radially emerging from the subdomain boundaries. Each obstacle is independently analyzed with the most appropriate technique and described through a generalized scattering matrix (GSM). Finally, a linear system is constructed, where the excitation vector is given by the complex source expansion of the primary sources. Thanks to the angular selectivity of the CPS beams, the subdomain interactions only involve a small fraction of the beams; thus, yielding sparse moderate size linear systems. Due to the re-usability of the GSMs, the proposed approach is particularly efficient in the context of parametric studies or antenna installation problems. Numerical examples are provided to demonstrate the efficiency and the accuracy of the proposed strategy.
2. Leopold, P. R., B. Felsen, and M. Mongiardo, "Electromagnetic field representations and computations in complex structures I: Complexity architecture and generalized network formulation," International Journal of Numerical Modelling: Electronic Net-works, Devices and Fields, Vol. 15, No. 1, 93-107, 2002.
doi:10.1002/jnm.433
3. Barka, A. and P. Caudrillier, "Domain decomposition method based on generalized scattering matrix for installed performance of antennas on aircraft ," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 6, 1833-1842, Jun. 2007.
doi:10.1109/TAP.2007.898602
4. Van de Water, A. M., B. P. de Hon, M. C. van Beurden, A. G. Tijhuis, and P. de Maagt, "Linear embedding via Green's operators: A modeling technique for finite electromagnetic band-gap structures," Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 72, No. 5, 056704, 2005.
5. Li, M.-K. and W. C. Chew, "Wave-field interaction with complex structures using equivalence principle algorithm," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 1, 130-138, Jan. 2007.
doi:10.1109/TAP.2006.888453
6. Nikolsky, V. V. and T. I. Nikolskaya, Decomposition Approach to the Problems of Electrodynamics, Nauka, National Bureau of Standards, Moscow, 1983.
7. D. M., Kerns, Plane-wave Scattering-matrix Theory of Antenna-antenna Interactions, Tech. Rep. NBS Monograph 162, Nat. Bur. Stand., 1981.
8. Elsherbeni, A. Z. and A. A. Kishk, "Modeling of cylindrical objects by circular dielectric and conducting cylinders," IEEE Transactions on Antennas and Propagation, Vol. 40, 96-99, Jan. 1992.
doi:10.1109/8.123363
9. Felbacq, D., G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," Journal of the Optical Society of America A, Vol. 11, 2526-2538, Sep. 1994.
doi:10.1364/JOSAA.11.002526
10. Peterson, B. and S. Strom, "T matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3)," Phys. Rev. D, Vol. 8, No. 10, 3661-3678, Nov. 1973.
doi:10.1103/PhysRevD.8.3661
11. Tsang, L., C. E. Mandt, and K. H. Ding, "Monte Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell's equations ," Optics Lett., Vol. 17, No. 5, 314-316, Mar. 1992.
doi:10.1364/OL.17.000314
12. Yan, W.-Z., Y. Du, Z. Li, E. Chen, and J. Shi, "Characterization of the validity region of the extended T-matrix method for scattering from dielectric cylinders with finite length ," Progress In Electromagnetics Research, Vol. 96, 309-328, 2009.
doi:10.2528/PIER09083101
13. Rubio, J., M. Gonzalez, and J. Zapata, "Generalized-scattering-matrix analysis of a class of finite arrays of coupled antennas by using 3-D fem and spherical mode expansion," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 3, 1133-1144, Mar. 2005.
doi:10.1109/TAP.2004.842687
14. Crocco, L., F. Cuomo, and T. Isernia, "Generalized scattering-matrix method for the analysis of two-dimensional photonic bandgap devices," J. Opt. Soc. Am. A, Vol. 24, No. 10, A12-A22, 2007.
doi:10.1364/JOSAA.24.000A12
15. Felsen, L. B., "Complex source point solution of the field equations and their relation to the propagation and scattering of Gaussian beams ," Symposia Mathematica, Vol. 18, 39-56, 1976.
16. Carli, G., E. Martini, and S. Maci, "Space decomposition method by using complex source expansion," Proc. IEEE Antennas and Propagation Society International Symposium 2008, Jul. 1-4, 2008.
17. Carli, G., E. Martini, M. Bandinelli, and S. Maci, "Domain decomposition and wave coupling by using complex source expansions," Proc. 3rd European Conference on Antennas and Propagation, EuCAP 2009, 2079-2082, Mar. 2009.
18. Tap, K., P. Pathak, and R. Burkholder, "Exact complex source point beam expansion of electromagnetic fields from arbitrary closed surfaces," Proc. IEEE Antennas and Propagation Society International Symposium 2007, 4028-4031, Jun. 2007.
doi:10.1109/APS.2007.4396424
19. Tap, K., P. Pathak, and R. Burkholder, "An exact CSP beam representation for EM wave radiation," International Conference on Electromagnetics in Advanced Applications, 75-78, Sep. 2007.
doi:10.1109/ICEAA.2007.4387242
20. Boag, A. and R. Mittra, "Complex multipole-beam approach to three-dimensional electromagnetic scattering problems," J. Opt. Soc. Am. A, Vol. 11, No. 4, 1505-1512, 1994.
doi:10.1364/JOSAA.11.001505
21. Erez, E. and Y. Leviatan, "Electromagnetic scattering analysis using a model of dipoles located in complex space," IEEE Transactions on Antennas and Propagation, Vol. 42, No. 12, 1620-1624, Dec. 1994.
doi:10.1109/8.362812
22. Tap, K., P. Pathak, and R. Burkholder, "Fast complex source point expansion for accelerating the method of moments," International Conference on Electromagnetics in Advanced Applications, 2007, ICEAA 2007, 986-989, Sep. 2007.
doi:10.1109/ICEAA.2007.4387472
23. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas and Propagation Magazine, Vol. 35, 7-12, 1993.
doi:10.1109/74.250128
24. Pozar, M., Microwave Engineering, 2 Ed., Wiley, New York, 1998.
25. Bucci, O. and G. Franceschetti, "On the degrees of freedom of scattered fields," IEEE Transactions on Antennas and Propagation, Vol. 37, No. 7, 918-926, Jul. 1989.
doi:10.1109/8.29386
26. Bucci, O., "Computational complexity in the solution of large antenna and scattering problems," Radio Sci., Vol. 40, 2005.
27. Stupfel, B. and Y. Morel, "Singular value decomposition of the radiation operator application to model-order and far-field reduction ," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 6, 1605-1615, Jun. 2008.
doi:10.1109/TAP.2008.923311
28. Leopardi, P., "A partition of the unit sphere into regions of equal area and small diameter," Electronic Transactions on Numerical Analysis, Vol. 25, 309-327, 2006.
29. Martini, E., G. Carli, and S. Maci, "An equivalence theorem based on the use of electric currents radiating in free space," Antennas and Wireless Propagation Letters, Vol. 11, 421-424, 2008.
doi:10.1109/LAWP.2008.2001764
30. Hansen, J. E., Spherical Near-field Antenna Measurements, Peter Peregrinus Ltd., London, 1988.
Submit
