A Fast Volume Integral Equation Solver for Electromagnetic Scattering from Large Inhomogeneous Objects in Planarly Layered Media

IEEE Transactions on Antennas and Propagation

Volumn 51, Issue 9, 2003, Pages 2393-2401

  Millard, Xuemin ^a   Liu, Qing Huo ^a  

^a USA   (United States)

Author keywords

Fast algorithm; Layered media; Scattering; Stabilized biconjugate gradient fast Fourier transform (BCGS FFT) method; Volume integral equation

Indexed keywords

ALGORITHMS; EMBEDDED SYSTEMS; FAST FOURIER TRANSFORMS; INTEGRAL EQUATIONS;

INHOMOGENEOUS OBJECTS;

ELECTROMAGNETIC WAVE SCATTERING;

EID: 0141526420     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2003.816311     Document Type: Article

References (25)

1. K. A. Michalski and D. Zheng, "Electromagnetic scattering and radiation by surface of arbitrary shape in layered media-Part I: Theory," IEEE Trans. Antennas Propagat., vol. 38, pp. 335-344, Mar. 1990.
2. _, "Electromagnetic scattering and radiation by surface of arbitrary shape in layered media-Part II: Implementation and results for contiguous half-space," IEEE Trans. Antennas Propagat., vol. 38, pp. 344-352, Mar. 1990.
3. K. A. Michalski and J. R. Mosig, "Multilayered media Green's functions in integral equation formulations," IEEE Trans. Antennas Propagat., vol. 45, pp. 508-519, Mar. 1997.
4. M. F. Catedra, E. Gago, and L. Nuno, "A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform," IEEE Trans. Antennas Propagat., vol. 37, pp. 528-537, May 1989.
5. P. Zwamborn and P. M. van den Berg, "The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems, " IEEE Trans. Microwave Theory Tech., vol. 9, pp. 1757-1766, Apr. 1992.
6. C. C. Su, "The three-dimensional algorithm of solving the electric field integral equation using face-centered node points, conjugate gradient method, and FFT," IEEE Trans. Microwave Theory Tech., vol. 41, pp. 510-515, Mar. 1993.
7. H. Gan and W. C. Chew, "A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatter problems," J. Electromagn. Waves Appl., vol. 9, no. 10, pp. 1339-1357, 1995.
8. Z. Q. Zhang and Q. H. Liu, "Three-dimensional weak-form conjugateand biconjugate-gradient FFT methods for volume integral equations," Microwave Opt. Tech. Lett., vol. 29, no. 5, pp. 350-356, June 2001.
9. Z. Q. Zhang, Q. H. Liu, and X. M. Xu, "RCS computation of large inhomogeneous objects using a fast integral equation solver," IEEE Trans. Antennas Propagat., vol. 51, pp. 613-618, Mar. 2003.
10. X. M. Xu, Q. H. Liu, and Z. Q. Zhang, "The stabilized biconjugate gradient fast Fourier transform method for electromagnetic scattering," J. Appl. Comput. Electromag. Soc., vol. 17, no. 1, pp. 97-103, Mar. 2002.
11. T. J. Cui and W. C. Chew, "Fast algorithm for electromagnetic scattering by buried 3-D dielectric objects of large size," IEEE Trans. Geosci. Remote Sensing, vol. 37, no. 5, pp. 2597-2608, Sept. 1999.
12. X. M. Xu and Q. H. Liu, "The BCGS-FFT method for electromagnetic scattering from inhomogeneous objects in a planarly layered medium," IEEE Antennas Wireless Propagat. Lett., vol. 1, pp. 77-80, 2002.
13. A. Sommerfeld, Partial Differential Equations. New York: Academic, 1949.
14. Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, "A closed-form spatial Green's function for the thick microstrip substrate," IEEE Trans. Microwave Theory Tech., vol. 43, pp. 588-592, July 1991.
15. M. I. Aksun, "A robust approach for the derivation of closed-form Green's function," IEEE Trans. Microwave Theory Tech., vol. 44, pp. 651-658, May 1996.
16. T. J. Cui and W. C. Chew, "Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three dimensional buried objects,"IEEE Trans. Geosci. Remote Sensing, vol. 37, pp. 887-900, Mar. 1997.
17. W. Cai and T. J. Yu, "Fast calculations of dyadic Green's functions for electromagnetic scattering in a multilayered medium," J. Computat. Phys., vol. 165, no. 1, pp. 1-21, Nov. 2000.
18. M. F. Catedra, E. Gago, and L. Nuno, "A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform," IEEE Trans. Antennas Propagat., vol. 37, pp. 528-537, May 1989.
19. H. A. van der Vorst, "Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems," SIAM J. Sci. Stat. Comput., vol. 13, no. 2, pp. 631-644, Mar. 1992.
20. M. R. Hestenes and E. Stiefel, "Methods of conjugate gradients for solving linear systems," J. Res. Nat. Bur. Stand., vol. 49, pp. 409-435, 1952.
21. T. K. Sarkar, "On the application of the generalized biconjugate gradient method," J. Electromagn. Waves Appl., vol. 1, no. 3, pp. 223-242, 1987.
22. P. Sonneveld, "COS: a fast Lanczos-type1 solver for nonsymmetric linear system," SIAM J. Sci. Statist. Comput., vol. 10, pp. 36-52, 1989.
23. R. W. Freund, "A transpose-free quasiminimal residual algorithm for nonHermitian linear systems," SIAMJ. Sci. Comput., vol. 14, no. 2, pp. 470-482, Mar. 1993.
24. Q. H. Liu, "An FDTD algorithm with perfectly matched layers for conductive media," Microwave Opt. Tech. Lett., vol. 14, no. 2, pp. 134-137, 1997.
25. J. He, A. Sullivan, and L. Carin, "Multilevel fast multipole algorithm for three-dimensional dielectric targets in the vicinity of a lossy half-space," Microwave Opt. Tech. Lett., vol. 29, pp. 100-104, Apr. 2001.