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 1, January 1999

A Pseudospectral Method for Time-Domain Computation of Electromagnetic Scattering by Bodies of Revolution

Page 132.

Abstract:

We present a multidomain pseudospectral method for the accurate and efficient time-domain computation of scattering by body-of-revolution (BOR) perfectly electrically conducting objects. In the BOR formulation of the Maxwell equations, the azimuthal dependence of the fields is accounted for analytically through a Fourier series. The numerical scheme in the (r,z) plane is developed in general curvilinear coordinates and the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution. A modified matched-layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time-domain boundary conditions along edges. Numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis-symmetric objects, including spheres, cone-spheres, and finite cylinders, is compared with results from the literature, illustrating the accuracy and computational efficiency associated with the use of properly constructed spectral methods. To emphasize the versatility of the presented framework, we compute plane wave scattering by a missile and find satisfactory agreement with method-of-moment (MoM) computations.

References

1. A. Taflove, Computational Electrodynamics--The Finite-Difference Time-Domain Method.Boston, MA: Artech House, 1995.
2. P. G. Petropoulous, "Phase error control for FDTD methods of second- and fourth-order accuracy," IEEE Trans. Antennas Propagat., vol. 42, pp. 859-862, June 1994.
3. B. Yang and D. Gottlieb, "Comparisons of staggered and nonstaggered schemes for Maxwell's equations," in Proc. 12th Annu. Rev. Progress Appl. Computat. Electromagn., Naval Postgraduate School, Monterey, CA, Mar. 1996, vol. II, pp. 1122-1131.
4. B. Yang, D. Gottlieb, and J. S. Hesthaven, "Spectral simulations of electromagnetic wave scattering," J. Comput. Phys., vol. 134, no. 2, pp. 216-230, 1997.
5. --, "On the use of PML ABC's in spectral time-domain simulations of electromagnetic scattering," in Proc. 13th Annu. Rev. Progress Appl. Computat. Electromagn., Naval Postgraduate School, Monterey, CA, Mar. 1997, vol. II, pp. 926-934.
6. D. Gottlieb, M. Gunzburger, and E. Turkel, "On numerical boundary treatment for hyperbolic systems," SIAM J. Numer. Anal., vol. 19, pp. 671-697, 1982.
7. J. Meixner, "The behavior of electromagnetic fields at egdes," IEEE Trans. Antennas Propagat., vol. AP-20, no. 4, pp. 442-446, July, 1972.
8. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics--Springer Series in Computational Physics.--New York: Springer-Verlag, 1987.
9. P. Fischer and D. Gottlieb, "On the optimal number of subdomains for hyperbolic problems on parallel computers," Int. J. Supercomputer Appl. High-Performance Comput., vol. 11, no. 1, pp. 65-76, 1997.
10. J. S. Hesthaven, "A stable penalty method for the compressible Navier-Stokes equations. II. One dimensional domain decomposition schemes," SIAM J. Sci. Comp., vol. 18, pp. 658-685, 1997.
11. W. J. Gordon and C. A. Hall, "Transfinite element methods: Blending-function interpolation over arbitrary curved element domains," Numer. Math., vol. 21, pp. 109-129, 1973.
12. J. S. Hesthaven, "A stable penalty method for the compressible Navier-Stokes equations. III. Multi dimensional domain decomposition schemes," SIAM J. Sci. Comp., to be published.
13. J. S. Shang, "Time-domain electromagnetic scattering simulations on multicomputers," J. Computat. Phys., vol. 128, no. 2, pp. 381-390, 1996.
14. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computat. Phys., vol. 114, pp. 185-200, 1994.
15. J. R. Mautz and R. F. Harrington, "Radiation and scattering from bodies of revolution," Appl. Sci. Res., vol. 20, pp. 405-435, 1969.
16. E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section.Boston, MA: Artech House, 1993.
17. J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes.New York: Hemisphere, 1987.
18. L. N. Medgyesi-Mitschang and D. Wang, "Hybrid solutions for scattering from perfectly conducting bodies of revolution," IEEE Trans. Antennas Propagat., vol. AP-31, pp. 570-583, June 1983.
19. S. D. Gedney and R. Mittra, "The use of the FFT for the efficient solution of the problem of electromagnetc scattering by a body of revolution," IEEE Trans. Antennas Propagat., vol. 38, no. 3, pp. 313-322, 1990.
20. J. S. Shang, private communication, 1997.