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2010-01-11

Sensitivity Analysis of 3-D Composite Structures through Linear Embedding via Green's Operators

By Vito Lancellotti, Bastiaan P. de Hon, and Antonius G. Tijhuis
Progress In Electromagnetics Research, Vol. 100, 309-325, 2010
doi:10.2528/PIER09120108

Abstract

We propose a methodology --- based on linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) --- for solving electromagnetic problems involving large 3-D structures comprised of ND ≥ 1 bodies. In particular, we address the circumstance when the electromagnetic properties or the shape of one body differ from those of the others. In real-life structures such a situation may be either the result of a thoughtful design process or the unwanted outcome of fabrication tolerances. In order to assess the sensitivity of physical observables to localized deviations from the "ideal" structure, we follow a deterministic approach, i.e., we allow for a finite number of different realizations of one of the bodies. Then, for each realization we formulate the problem with LEGO and we employ the EEM to determine the contribution of the ND - 1 "fixed" bodies. Since the latter has to be computed only once, the overall procedure is indeed efficient. As an example of application, we investigate the sensitivity of a 2-layer array of split-ring resonators with respect to the shape and the offset of one element in the array.

Citation


Vito Lancellotti, Bastiaan P. de Hon, and Antonius G. Tijhuis, "Sensitivity Analysis of 3-D Composite Structures through Linear Embedding via Green's Operators," Progress In Electromagnetics Research, Vol. 100, 309-325, 2010.
doi:10.2528/PIER09120108
http://jpier.org/PIER/pier.php?paper=09120108

References


    1. Engheta, N., W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, "The fast multipole method (FMM) for electromagnetic problems," IEEE Trans. Antennas Propag., Vol. 40, 634-641, Jun. 1992.
    doi:10.1109/8.144597

    2. Song, J. M., C. C. Lu, and W. C. Chew, "MLFMA for electromagnetic scattering from large complex objects," IEEE Trans. Antennas Propag., Vol. 45, 1488-1493, Oct. 1997.
    doi:10.1109/8.633855

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

    4. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, , IEEE Press, Piscataway, 1998.

    5. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, New York, 1989.

    6. Peng, Z. Q. and A. G. Tijhuis, "Transient scattering by a lossy dielectric cylinder: Marching-on-in-frequency approach," Journal of Electromagnetic Waves and Applications, Vol. 7, No. 5, 1993.
    doi:10.1163/156939393X00840

    7. Tijhuis, A. G., M. C. Beurden, and A. P. M. Van Zwamborn, "Iterative solution of field problems with a varying physical parameter," Elektrik, Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 10, No. 2, 2002.

    8. Yeo, J., V. V. S. Prakash, and R. Mittra, "Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM)," Microwave and Optical Technology Letters, Vol. 39, No. 6, 456-464, 2003.
    doi:10.1002/mop.11247

    9. Mittra, R. and K. Du, "Characteristic basis function method for iteration-free solution of large method of moments problems," Progress In Electromagnetics Research B, Vol. 6, 307-336, 2008.
    doi:10.2528/PIERB08031206

    10. Li, M. K. and W. C. Chew, "Wave-field interaction with complex structures using equivalence principle algorithm," IEEE Trans. Antennas Propag., Vol. 55, 130-138, Jan. 2007.
    doi:10.1109/TAP.2006.888453

    11. Matekovitz, L., V. A. Laza, and G. Vecchi, "Analysis of large complex structures with the synthetic-functions approach," IEEE Trans. Antennas Propag., Vol. 55, 2509-2521, Sep. 2007.
    doi:10.1109/TAP.2007.904073

    12. Yuan, H.-W., S.-X. Gong, Y. Guan, and D.-Y. Su, "Scattering analysis of the large array antennas using the synthetic basis functions method," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 2-3, 309-320, 2009.
    doi:10.1163/156939309787604364

    13. Yla-Oijala, P. and M. Taskinen, "Electromagnetic scattering by large and complex structures with surface equivalence principle algorithm," Waves in Random and Complex Media, Vol. 19, 105-125, Feb. 2009.
    doi:10.1080/17455030802585365

    14. Xiao, G., J.-F. Mao, and B. Yuan, "A generalized surface integral equation formulation for analysis of complex electromagnetic systems," IEEE Trans. Antennas Propag., Vol. 57, 701-710, Mar. 2009.
    doi:10.1109/TAP.2009.2013425

    15. Laviada, J., F. Las-Heras, M. R. Pino, and R. Mittra, "Solution of electrically large problems with multilevel characteristic basis functions," IEEE Trans. Antennas Propag., Vol. 57, 3189-3198, Oct. 2009.

    16. Golub, G. H. and C. F. V. Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 1996.

    17. 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," Phys. Rev. E, Vol., Vol. 72, 1-11, Nov. 2005.

    18. Lancellotti, V., B. P. De Hon, and A. G. Tijhuis, "An eigencurrent approach to the analysis of electrically large 3-D structures using linear embedding via Green's operators," IEEE Trans. Antennas Propag., Vol. 57, 3575-3585, Nov. 2009.

    19. Lancellotti, V., B. P. De Hon, and A. G. Tijhuis, "On the convergence of the eigencurrent expansion method applied to linear embedding via Green's operators,", submitted Oct. 2009.

    20. Bekers, D. J., S. J. L. Van Eijndhoven, and A. G. Tijhuis, "An eigencurrent approach for the analysis of finite antenna arrays," IEEE Trans. Antennas Propag., Vol. 58, Dec. 2009.

    21. Lancellotti, V., B. P. De Hon, and A. G. Tijhuis, "A total inverse scattering operator formulation for the analysis of large 3-D structures," 11th ICEAA, Torino, Italy, Sept. 2009.

    22. Lancellotti, V., B. P. De Hon, and A. G. Tijhuis, "Analysis of antennas in the presence of large composite 3-D structures with linear embedding via Green's operators (LEGO) and a modified EFIE," 4th EuCAP, Barcelona, Spain, to be presented, Apr. 2010.

    23. Lindell, I., "Huygens' principle in electromagnetics," Science, Measurement and Technology, IEE Proceedings, Vol. 143, 103-105, Mar. 1996.
    doi:10.1049/ip-smt:19960218

    24. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, 409-418, May 1982.
    doi:10.1109/TAP.1982.1142818

    25. Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. D. Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users' Guide, SIAM, 1999.

    26. Gurel, L., O. Ergul, and A. Unal, "Accurate analysis of metamaterials involving finite arrays of split-ring resonators and thin wires," PIERS Proceedings, 470-473, Beijing, China.

    27. Ergul, O., T. Malas, C. Yavuz, A. Unal, and L. Gurel, "Computational analysis of complicated metamaterial structures using MLFMA and nested preconditioners," 2nd EuCAP, Edinburg, UK, Nov. 2007.