volume | PIER Journals

Abstract

An innovative preconditioner has been developed in this work. It significantly improves the convergence of the iterative solvers applied to electromagnetic radiation problems by a renormalization of the matrix equation. The preconditioner balances the disparities in terms of magnitude and units caused by the strong self-coupling of the antennas, the non-uniformity of the meshes and also by the coexistence of wire and surface basis functions. It can be easily integrated into different electromagnetic solvers with a negligible impact on the computational cost on account of its simple implementation.

1. Harrington, R. F., Field Computation by Moment Method, IEEE Press, 1993.

2. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, No. 3, 409-418, 1982.
doi:10.1109/TAP.1982.1142818 Google Scholar

3. Hwu, S. U., D. R. Wilton, and S. M. Rao, "Electromagnetic scattering and radiation by arbitrary conducting wire/surface configurations," IEEE Int. Antennas and Porpagat. Symp., Vol. 26, 890-893, 1998. Google Scholar

4. Coifman, R., V. Rokhlin, and S. Wanzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propagat. Mag. , Vol. 35, No. 3, 7-12, 1993.
doi:10.1109/74.250128 Google Scholar

5. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," EEE Trans. Antennas Propagat., Vol. 45, 1488-1493, 1997.
doi:10.1109/8.633855 Google Scholar

6. Pan, X. M. and X. Q. Sheng, "A highly efficient parallel approach of multi-level fast multipole algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 8, 1081-1092, 2006.
doi:10.1163/156939306776930321 Google Scholar

7. Wang, P. and Y. J. Xie, "Scattering and radiation problem of surface/surface junction structure with multilevel fast multipole algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 15, 2189-2200, 2006.
doi:10.1163/156939306779322567 Google Scholar

8. Fan, Z. H., D. Z. Ding, and R. S. Chen, "The efficient analysis of electromagnetic scattering from composite structures using hybrid CFIE-IEFIE," Progress In Electromagnetics Research B, Vol. 10, 131-143, 2008.
doi:10.2528/PIERB08091606 Google Scholar

9. Hesford, A. J. and W. C. Chew, "On preconditioning and the eigensystems of electromagnetic radiation problems," IEEE Trans. Antennas Propagat., Vol. 56, No. 8, 2413-2420, 2008.
doi:10.1109/TAP.2008.926783 Google Scholar

10. Lee, J., J. Zhang, and C. C. Lu, "Sparse inverse preconditioning Sparse inverse preconditioning in electromagnetics," IEEE Trans. Antennas Propagat., Vol. 52, No. 9, 2277-2287, 2004.
doi:10.1109/TAP.2004.834084 Google Scholar

11. Rui, P. L. and R. S. Chen, "An efficient sparse approximate inverse preconditioning for FMM implementation," Microwave and Optical Technology Letters, Vol. 49, No. 7, 1746-1750, 2007.
doi:10.1002/mop.22538 Google Scholar

12. Ding, D. Z., R. S. Chen, and Z. Fan, "An efficient sai preconditioning technique for higher order hierarchical MLFMM implementation," Progress In Electromagnetics Research, PIER 88, 255-273, 2008. Google Scholar

13. Sertel, K. and J. L. Volakis, "Incomplete LU preconditioner for FMM implementation," Microwave and Optical Technology Letters, Vol. 26, No. 7, 265-267, 2000.
doi:10.1002/1098-2760(20000820)26:4<265::AID-MOP18>3.0.CO;2-O Google Scholar

14. Heldring, A., J. M. Rius, and L. Ligthart, "New block ILU preconditioner scheme for numerical analysis of very large electromagnetic problems," IEEE Trans. Magn., Vol. 38, No. 2, 337-346, 2002.
doi:10.1109/20.996091 Google Scholar

15. Benzi, M., "Preconditioning techniques for large linear systems: A survey," J. Comput. Phys., No. 182, 418-477, 2002.
doi:10.1006/jcph.2002.7176 Google Scholar

16. Ergul, O. and L. Gurel "Efficient solution of the electric-field integral equation using the iterative LSQR algorithm," IEEE Antennas Wireless Propagat. Lett., Vol. 7, 36-39, 2008. Google Scholar

17. Andriulli, F. P., et al., "A multiplicative calderon preconditioner for the electric field integral equation," IEEE Trans. Antennas Propagat., Vol. 56, No. 8, 2398-2412, 2008.
doi:10.1109/TAP.2008.926788 Google Scholar

18. Saad, Y., Iterative Methods for Sparse Linear Systems, PWS Publishing Company, a division of International Thomsom Publishing Inc., 1996.

19. Makarov, S., "MoM antenna simulations with matlab: RWG basis functions," IEEE Antennas Propagat. Mag., Vol. 43, No. 5, 100-107, 2001.
doi:10.1109/74.979384 Google Scholar

Miss Marta Gomez Araujo

Dr. Jose Manuel Bertolo

Professor Fernando Obelleiro

Prof. Jose Luis Rodriguez

Dr. Jose Taboada

Prof. Luis Landesa