1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Antennas and Propagation
Volume 47 Number 9, September 1999

An Iterative Algorithm Based on the Measured Equation of Invariance for the Scattering Analysis of Arbitrary Multicylinders

Page 1463.

Abstract:

It is known that the measured equation of invariance (MEI) is generally valid for outgoing waves just as other absorbing boundary conditions (ABC's). However, for the scattering problem of multicylinders, the scattered field from one cylinder is just the in-going incident wave to other cylinders. So the MEI cannot be directly applied to the scattering problem of multicylinders. In this paper, an iterative algorithm based on the MEI is first proposed for the scattering problems of multicylinders with arbitrary geometry and physical parameters. Each cylinder is coated with several layers of meshes and the MEI's are applied to the truncated mesh boundaries. It has been demonstrated that the MEI can truncate the meshes very close to the surfaces of the cylinders and then results in dramatically savings in memory requirements and computational time. The MEI coefficients of each cylinder can be stored and reused to form the sparse matrices during each iteration procedure as they are independent of excitations. So more central processing unit (CPU) time is saved as the MEI coefficients are calculated only once in the algorithm. The method can be applied to problems of various kinds of multiple cylinders with arbitrary configurations and cross sections. Numerical results for the scattered fields are in good agreement with the data available. Finally, examples are given to show the iterative algorithm applicable to electrically large multicylinders coated with lossy media.

References

1. V. Twersky, "Multiple scattering of radiation by an arbitrary configuration of parallel cylinders," J. Acoust. Soc. Amer., vol. 24, pp. 42-46, 1952.
2. C. R. Mullin, R. Sandburg, and C. O. Velline, "A numerical technique for the determination of scattering cross sections of infinite cylinders of arbitrary geometrical cross section," IEEE Trans. Antennas Propagat., vol. AP-13, pp. 141-149, Mar. 1965.
3. N. Zitoron and S. N. Karp, "Higher order approximation in multiple scattering I: Two-dimensional scalar case," J. Math. Phys., vol. 2, pp. 394-402, 1961.
4. K. Hongo, "Multiple scattering by two conducting circular cylinders," IEEE Trans. Antennas Propagat., vol. AP-26, pp. 748-751, Sept. 1978.
5. J. W. Young and J. C. Bertrand, "Multiple scattering by two cylinders," J. Aoust. Soc. Amer., vol. 58, pp. 1190-1195, 1975.
6. H. Ragheb and M. Hamid, "Scattering by N parallel conducting circular cylinders," Int. J. Electromagn., vol. 59, pp. 407-421, 1985.
7. A. Z. Elsherbeni and M. Hamid, "Scattering by parallel conducting circular cylinders," IEEE Trans. Antennas Propagat., vol. AP-35, pp. 355-358, Mar. 1987.
8. M. G. Andreasen, "Scattering from parallel metallic cylinders with arbitrary cross sections," IEEE Trans. Antennas Propagat., vol. AP-12, pp. 746-754, Nov. 1964.
9. A. A. Kishk and L. Shafai, "Different formulations for numerical solution of single and multibodies of revolution with mixed boundary conditions," IEEE Trans. Antennas Propagat., vol. AP-34, pp. 666-673, May 1986.
10. G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat., vol. EMC-23, pp. 377-382, Nov. 1981.
11. K. K. Mei, R. Pous, Z. Q. Chen, and Y. W. Liu, "The measured equation of invariance: A new concept in field computation," IEEE Trans. Antennas and Propagat., vol. 42, pp. 320-327, Mar. 1994.
12. W. Hong, Y. W. Liu, and K. K. Mei, "Application of the measured equation of invariance to solve scattering problems involving penetrable medium," Radio Sci., vol. 29, no. 4, pp. 897-906, 1994.
13. R. Pous, M. D. Prouty, and K. K. Mei, "Application of the measured equation of invariance to radiation and scattering by flat surfaces," in IEEE AP-S Symp. Dig., Ann Arbor, MI, p. 540, July 1993.
14. M. D. Prouty, R. Pous, K. K. Mei, and S. E. Schwartz, "Application of the measured equation of invariance to transmission lines and discontinuities," IEEE AP-S Symp. Dig. Ann Arbor, MI, p. 280, July 1993.
15. J. Chen, W. Hong, and J. Jin, "An iterative measured equation technique for electromagnetic problems," IEEE Trans. Microwave Theory Tech. vol. 46, pp. 25-30, Jan. 1998.