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IEEE Transactions on Antennas and Propagation
Volume 46 Number 3, March 1998

On the Canonical Grid Method for Two-Dimensional Scattering Problems

Page 297.

Abstract:

The banded matrix iterative approach with a canonical grid expansion (BMIA/CAG) has been shown in [1] to be an efficient method for the calculation of scattering for near planar two-dimensional (2-D) geometries such as one-dimensional rough surfaces. However, in [1], only the first three terms in the canonical grid series for TE polarization above a perfectly conducting surface were discussed and methods for implementing only a portion of these terms were presented. In this paper, a general form for all terms in the canonical grid series is provided for both TE and TM polarizations above an impedance surface and an efficient algorithm for calculating their contributions is described. The relationship between the canonical grid and operator expansion methods is also discussed. A sample surface scattering problem is shown to illustrate the utility of higher order terms in the canonical grid method.

References

1. L. Tsang, C. H. Chan, K. Pak, and H. Sangani, "Monte Carlo simulations of large scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method," IEEE Trans. Antennas Propagat., vol. 43, pp. 851-859, 1995.
2. D. A. Kapp and G. S. Brown, "A new numerical method for rough surface scattering calculations," IEEE Trans. Antennas Propagat., vol. 44, pp. 711-721, 1996.
3. D. Holliday, L. L. Deraad, and G. J. St-Cyr, "Forward-backward: A new method for computing low grazing angle scattering," IEEE Trans. Antennas Propagat., vol. 44, pp. 722-729, 1996.
4. D. M. Milder, "An improved formalism for wave scattering from rough surfaces," J. Acoust. Soc. Amer., vol. 89, pp. 529-541, 1991.
5. N. Engheta, W. D. Murphy, V. Rokhlin, and M. S. Vassiliou, "The fast multipole method for electromagnetic scattering problems," IEEE Trans. Antennas Propagat., vol. 40, pp. 634-641, 1992.
6. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, "A fast integral equation solver for electromagnetic scattering problems," in IEEE APS/URSI Symp. Conf. Proc., 1994, pp. 416-419.
7. J. A. Kong, Electromagnetic Wave Theory, 2nd ed.New York: Wiley, 1990.
8. K. M. Mitzner, "An integral equation approach to scattering from a body of finite conductivity," Radio Sci., vol. 2, pp. 1459-1470, 1967.
9. R. F. Harrington, Field Computation by Moment Methods.New York: Macmillan, 1968.
10. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., A. Jeffrey, Ed.San Diego, CA: Academic, 1994.
11. J. T. Johnson, R. T. Shin, J. Eidson, L. Tsang, and J. A. Kong, "A method of moments model for VHF propagation," IEEE Trans. Antennas Propagat., vol. 45, pp. 115-125, 1997.
12. P. J. Kaczkowski and E. I. Thorsos, "Application of the operator expansion method to scattering from one-dimensional moderately rough Dirichlet random surfaces," J. Acoust. Soc. Amer., vol. 96, pp. 957-966, 1994.
13. E. I. Thorsos, "Acoustic scattering from Pierson-Moskowitz sea surfaces," J. Acoust. Soc. Amer., vol. 88, pp. 335-349, 1990.
14. L. A. Klein and C. T. Swift, "An improved model for the dielectric constant of sea water at microwave frequencies," IEEE Trans. Antennas Propagat., vol. 25, pp. 104-111, 1977.