PIER | |
Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |
Home > Vol. 81 > pp. 303-314
ADAPTIVELY ACCELERATED GMRES FAST FOURIER TRANSFORM METHOD FOR ELECTROMAGNETIC SCATTERINGBy Y. F. Xin and P.-L. RuiAbstract: 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:
References:
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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 13. Morgan, R. B., "GMRES with deflated restarting," SIAM J. Sci. Comput., Vol. 24, 20-37, 2002. 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. 15. Erhel, J., K. Burrage, and B. Pohl, "Restarted GMRES preconditioned by deflation," J. Comput. Appl. Math., Vol. 69, 303-318, 1996. 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. 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. 18. Saad, Y., "A flexible inner-outer preconditioned GMRES algorithm," SIAM J. Sci. Comput., Vol. 14, No. 2, 461-469, 1993. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. |