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IEEE Transactions on Antennas and Propagation
Volume 46 Number 8, August 1998

Electromagnetic Scattering from 3-D Curved Dielectric Bodies Using Time-Domain Integral Equations

Page 1212.

Abstract:

A boundary integral equation (BIE) approach is developed to calculate transient scattering from dielectric bodies. The treatment is directly in terms of the E and H fields rather than magnetic and electric currents. It employs curvilinear (quadratic) modeling, which allows accurate representation of arbitrarily shaped curved bodies. The treatment is isoparametric with the same quadratic representation of the spatial field variation and with the temporal variation modeled by similar quadratic elements. Integration employs high-order Gaussian quadrature with special treatment of the singular and hypersingular integrals that arise. The treatment is implicit, requiring the solution of a sparse matrix equation at each timestep. This adds only trivially to the cost at each timestep and, by freeing the timestep from the constraint that it be smaller than the smallest nodal spacing, can greatly reduce the number of timesteps that must be employed. Additionally, it produces stable results without resort to the averaging processes proposed elsewhere. Example calculations of scattering from a sphere, a cube, and an almond are presented and compared with earlier published transient results and with results from a frequency domain treatment. Good agreement and improved accuracy is found.

References

1. E. K. Miller, "A selective survey of computational electromagnetics," IEEE Trans. Antennas Propagat., vol. 36, pp. 1281-1305, Sept.1988.
2. A. J. Poggio and E. K. Miller, "Integral equation methods of three-dimensional scattering problems," in Computer Techniques for Electromagnetics, R. Mittra, Ed.Oxford, U.K.: Pergamon, 1973, pp. 159-265.
3. S. M. Rao and D. R. Wilton, "Transient scattering by conducting surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., vol. 39, pp. 56-61, Jan. 1991.
4. B. P. Rynne, "Time-domain scattering from arbitrary surfaces using the electric field integral equation," Electromagn. Waves Applicat., vol. 5, pp. 93-112, 1991.
5. M. J. Bluck and S. P. Walker, "Time-domain BIE analysis of large three-dimensional electromagnetic scattering problems," IEEE Trans. Antennas Propagat., vol. 45, pp. 894-901, May 1997.
6. H. Mieras and C. L. Bennett, "Space-time integral equation approach to dielectric targets," IEEE Trans. Antennas Propagat., vol. AP-30, pp. 2-9, Jan. 1982.
7. B. P. Rynne, "Time domain scattering from dielectric bodies," Electromagn., vol. 14, pp. 181-193, 1994.
8. D. A. Vechinski, S. M. Rao, and T. K. Sarkar, "Transient scattering from three-dimensional arbitrary shaped dielectric bodies," J. Opt. Soc. Amer., vol. 11, pp. 1458-1470, 1994.
9. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., vol. AP-30, pp. 409-418, Mar. 1982.
10. A. C. Woo, H. T. G. Wang, and M. J. Schuh, "Benchmark radar targets for the validation of computational electromagnetics programs," IEEE Antennas Propagat. Mag., vol. 35, pp. 84-89, Feb. 1993.
11. R. F. Harrington, Field Computation by Moment Methods.New York: MacMillan, 1968.
12. E. Marx, "Integral equation for scattering by a dielectric," IEEE Trans. Antennas Propagat., vol. AP-32, pp. 166-172, Feb. 1984.
13. J. C. Lachat and J. O. Watson, "Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics," Int. J. Numer. Methods Eng., vol. 10, pp. 991-1005,1976.
14. M. J. Bluck, M. D. Pocock, and S. P. Walker, "An accurate method for the calculation of singular integrals arising in time-domain integral equation analysis of electromagnetic scattering," IEEE Trans. Antennas Propagat., vol. 45, pp. 1793-1798, Dec. 1997.
15. M. J. Bluck, "Integral equation methods for transient wave propagation," Ph.D. dissertation, Univ. London, U.K., 1993.
16. M. J. Bluck and S. P. Walker, "Analysis of three dimensional transient acoustic wave propagation using the boundary integral equation method," Int. J. Numer. Methods Eng., vol. 39, pp. 1419-1431,1996.
17. S. P. Walker and C. Y. Leung, "Parallel computation of integral equation methods for three dimensional transient wave propagation," Commun. Numer. Methods Eng., vol. 11, pp. 515-524, 1995.
18. M. D. Pocock and S. P. Walker, "Radar cross Section prediction using boundary integral equation methods with isoparametric quadratic surface modeling and iterative solvers," Electromagn., vol. 16, pp. 651-669, 1996.