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Progress In Electromagnetics Research
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ADAPTIVELY ACCELERATED GMRES FAST FOURIER TRANSFORM METHOD FOR ELECTROMAGNETIC SCATTERING

By Y. F. Xin and P.-L. Rui

Full Article PDF (333 KB)

Abstract:
The problem of electromagnetic scattering by 3D dielectric bodies is formulated in terms of a weak-form volume integral equation. Applying Galerkin's method with rooftop functions as basis and testing functions,the integral equation can be usually solved by Krylov-subspace fast Fourier transform (FFT) iterative methods. In this paper,the generalized minimum residual (GMRES)-FFT method is used to solve this integral equation,and several adaptive acceleration techniques are proposed to improve the convergence rate of the GMRES-FFT method. On several electromagnetic scattering problems,the performance of these adaptively accelerated GMRESFFT methods are thoroughly analyzed and compared.

Citation:
Y. F. Xin and P.-L. Rui, "Adaptively accelerated GMRES fast fourier transform method for electromagnetic scattering," Progress In Electromagnetics Research, Vol. 81, 303-314, 2008.
doi:10.2528/PIER08011603
http://www.jpier.org/PIER/pier.php?paper=08011603

References:
1. Harrington, R. F., Field Computation by Moment Method, Kriegr, Melbourne, FL, 1968.

2. Bojarski, N. N., "The k-space formulation of the scattering problem in the time domain," J. Acoust. Soc. Amer., Vol. 72, 570-584, 1982.
doi:10.1121/1.388038

3. Zwamborn, A. P. M. and P. M. van den Berg, "The threedimensional weak form of the conjugate gradient FFT method for solving scattering problems," IEEE Trans. Microwave Theory Tech., Vol. 40, No. 9, 1757-1766, 1992.
doi:10.1109/22.156602

4. Zhang, Z. Q. and Q. H. Liu, "Three-dimensional weak-form conjugate-and biconjugate-gradient FFT methods for volume integral equations," Microwave Opt. Tech. Lett., Vol. 29, No. 5, 350-356, 2001.
doi:10.1002/mop.1176

5. Zhang, Z. Q., 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, No. 3, 2003.
doi:10.1109/TAP.2003.808536

6. Chen, R. S., et al., "Analysis of electromagnetic scattering of three dimensional dielectric bodies by use of Krylov-subspace FFT iterative methods," Microwave and Optical Technology Letters, Vol. 39, No. 4, 261-267, 2003.
doi:10.1002/mop.11186

7. Rui, P. L., et al., "Fast analysis of electromagnetic scattering of 3D dielectric bodies with augmented GMRES-FFT method," IEEE Trans. Antennas Propagat., Vol. 53, No. 11, 3848-3852, 2005.
doi:10.1109/TAP.2005.858833

8. Rui, P . L. and R. S. Chen, "Implicitly restarted GMRES fast Fourier transform method for electromagnetic scattering," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 7, 973-986, 2007.
doi:10.1163/156939307780748968

9. Saad, Y. and M. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM Journal on Scientific and Statistical Computing, Vol. 7, 856-869, 1986.
doi:10.1137/0907058

10. Joubert, W., "On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems," Numerical Linear Algebra with Application, Vol. 1, 427-447, 1994.
doi:10.1002/nla.1680010502

11. Morgan, R. B., "A restarted GMRES method augmented with eigenvectors," SIAM Journal on Scientific and Statistical Computing, Vol. 16, No. 4, 1154-1171, 1995.

12. Morgan, R. B., "Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems equations," SIAM J. Matrix Anal. Appl., Vol. 21, 1112-1135, 2000.
doi:10.1137/S0895479897321362

13. Morgan, R. B., "GMRES with deflated restarting," SIAM J. Sci. Comput., Vol. 24, 20-37, 2002.
doi:10.1137/S1064827599364659

14. Kharchenko, S. A. and A. Y. Yeremin, "Eigenvalue translation based preconditioners for the GMRES (k) method," Num. Lin. Alg. with Appl., Vol. 2, 51-77, 1995.
doi:10.1002/nla.1680020105

15. Erhel, J., K. Burrage, and B. Pohl, "Restarted GMRES preconditioned by deflation," J. Comput. Appl. Math., Vol. 69, 303-318, 1996.
doi:10.1016/0377-0427(95)00047-X

16. Baker, A. H., E. R. Jessup, and T. Manteuffel, "A technique for accelerating the convergence of restarted GMRES," SIAM J. Matrix Anal. Appl., Vol. 26, No. 4, 962-984, 2005.
doi:10.1137/S0895479803422014

17. Van der Vort, H. A. and C. Vuik., "GMRESR: A family of nested GMRES methods," Num. Lin. Alg. with Appl., Vol. 1, No. 4, 369-386, 1994.
doi:10.1002/nla.1680010404

18. Saad, Y., "A flexible inner-outer preconditioned GMRES algorithm," SIAM J. Sci. Comput., Vol. 14, No. 2, 461-469, 1993.
doi:10.1137/0914028

19. Jeong, Y. S. and J. H. Lee, "Estimation of time delay using conventional beamforming-based algorithm for UWB systems," Joural of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2413-2420, 2007.
doi:10.1163/156939307783134281

20. Betzios, P . V., I. S. Karanasiou, and N. K. Uzunoglu, "Analysis of a dielectric resonator antenna by applying a combined semianalytical method and simulation," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1983-1994, 2007.
doi:10.1163/156939307783152795

21. Li, L. and Y. Xie, "Efficient algorithm for analyzing microstrip antennas using fast-multipole algorithm combined with fixed realimage simulated method," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 15, 2177-2188, 2006.
doi:10.1163/156939306779322521

22. Carpentieri, B., "Fast large RCS calculation using the boundary element method," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1959-1968, 2007.
doi:10.1163/156939307783152768

23. Zou, Y. L., J. Y. Li, and Q. Z. Liu, "Mo dified mode decomposition for analyzing antennas with body of revolution radome," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 10, 1403-1410, 2007.
doi:10.1163/156939307783239519

24. Edee, K., G. Granet, R. Dusseaux, and C. Baudier, "A hybrid method for the study of plane waves scattering by rough surfaces," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 8, 1001-1015, 2004.
doi:10.1163/1569393042955423

25. Liu, X., B.-Z. Wang, and S. Lai, "Element-free Galerkin method in electromagnetic scattering field computation," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 14, 1915-1923, 2007.
doi:10.1163/156939307783152920

26. Ruppin, R., "Scattering of electromagnetic radiation by a perfect electromagnetic conductor cylinder," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1853-1860, 2006.
doi:10.1163/156939306779292219

27. Zhang, Y.-J. and E.-P. Li, "Scattering of three-dimensional chiral objects above a perfect conducting plane by hybrid finite element method," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 11, 1535-1546, 2005.
doi:10.1163/156939305775701813

28. Guo, J.-L., J.-Y. Li, and Q.-Z. Liu, "Electromagnetic analysis of coupled conducting and dielectric targets using MOM with a preconditioner," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 9, 1223-1236, 2005.
doi:10.1163/156939305775526007


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