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IEEE Transactions on Antennas and Propagation
Volume 46 Number 5, May 1998

Table of Contents for this issue

Complete paper in PDF format

Recursive T-Matrix Methods for Scattering from Multiple Dielectric and Metallic Objects

Adnan S}ahin and Eric L. Miller, Member, IEEE

Page 672.

Abstract:

We present an efficient, stable, recursive T-matrix algorithm to calculate the scattered field from a heterogeneous collection of spatially separated objects. The algorithm is based on the use of higher order multipole expansions than those typically employed in recursive T-matrix techniques. The use of these expansions introduces instability in the recursions developed in [5] and [6], specifically in the case of near-field computations. By modifying the original recursive algorithm to avoid these instabilities, we arrive at a flexible and efficient forward solver appropriate for a variety of scattering calculations. The algorithm can be applied when the objects are dielectric, metallic, or a mixture of both. We verify this method for cases where the scatterers are electrically small (fraction of a wavelength) or relatively large ( 1-2\lambda). While developed for near-field calculation, this approach is applicable for far-field problems as well. Finally, we demonstrate that the computational complexity of this approach compares favorably with comparable recursive algorithms.

References

  1. R. F. Harrington, Field Computation by Moment Methods.New York: IEEE Press, 1993; originally, Malabar, FL: Krieger, 1968.
  2. V. Rokhlin, "Rapid solution of integral equations of scattering theory in two dimensions," J. Computat. Phys., vol. 86, no. 2, pp. 414-439, 1990.
  3. P. C. Waterman, "New formulation of acoustic scattering," J. Acoust. Soc., vol. 45, no. 6, pp. 1417-1429, 1969.
  4. B. Peterson and S. Ström, "Matrix formulation of acoustic scattering from an arbitrary number of scatterers," J. Acoust. Soc. Amer., vol. 56, no. 3, pp. 771-780, Sept. 1974.
  5. W. C. Chew, Waves and Fields in Inhomogeneous Media.New York: Van Nostrand Reinhold, 1990.
  6. Y. M. Wang and W. C. Chew, "An efficient algorithm for solution of a scattering problem," Microwave Opt. Technol. Lett., vol. 3, no. 3, pp. 102-106, Mar. 1990.
  7. W. C. Chew, J. A. Friedrich, and R. Geiger, "A multiple scattering solution for effective permittivity of a sphere mixture," IEEE Trans. Geosci. Remote Sensing, vol. 28, no. 2, pp. 207-214, Mar. 1990.
  8. W. C. Chew, L. Gürel, Y. M. Wang, G. Otto, R. L. Wagner, and Q. H. Liu, "A generalized recursive algorithm for wave-scattering solutions in two dimensions," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 716-722, Apr. 1992.
  9. W. C. Chew and Y. M. Wang, "A fast algorithm for solution of a scattering problem using a recursive aggregate \tau matrix method," Microwave Opt. Technol. Lett., vol. 3, no. 5, pp. 164-169, May 1990.
  10. W. C. Chew, Y. M. Wang, and L. Gürel, "Recursive algorithm for wave-scattering solutions using windowed addition theorem," J. Electromagn. Waves Applicat., vol. 6, no. 11, pp. 1537-1560, 1992.
  11. L. Gürel and W. C. Chew, "A recursive T-matrix algorithm for strips and patches," Radio Sci., vol. 27, pp. 387-401, May/June 1992.
  12. --, "Scattering solution of three-dimensional array of patches using the recursive T-matrix algorithms," IEEE Microwave Guided Wave Lett., vol. 2, pp. 182-184, May 1992.
  13. A. Sahin and E. L. Miller, "Recursive T-matrix algorithm for multiple metallic cylinders," Microwave Opt. Technol. Lett., vol. 15, no. 6, pp. 360-363, Aug. 1997.
  14. M. Ouda, M. Hussein, and A. Sebak, "Multiple scattering by dielectric cylinders using a multi-filament current model," J. Electromagn. Waves Applicat., vol. 7, no. 2, pp. 215-234, 1993.
  15. J. E. Molyneux and A. Witten, "Diffraction tomographic imaging in a monostatic measurement geometry," IEEE Trans. Geosci. Remote Sensing, vol. 31, pp. 507-511, Mar. 1993.
  16. A. J. Witten and J. E. Molyneux, "Ground penetrating radar tomography: Algorithms and case studies," IEEE Trans. Geosci. Remote Sensing, vol. 32, pp. 461-467, Mar. 1994.
  17. R. W. Deming and A. J. Devaney, "A filtered backpropagation algorithm for GPR," J. Environmental Eng. Geophys., vol. 0, no. 2, pp. 113-123, Jan. 1996.