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Progress In Electromagnetics Research
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APPLICATION OF TWO-STEP SPECTRAL PRECONDITIONING TECHNIQUE FOR ELECTROMAGNETIC SCATTERING IN A HALF SPACE

By D.-Z. Ding, R.-S. Chen, and Z. Fan

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Abstract:
To efficiently solve large dense complex linear system arising from electric field integral equations (EFIE) formulation of half-space electromagnetic scattering problems, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix-vector product operations. The two-step spectral preconditioning is developed for the generalized minimal residual iterative method (GMRES). The two-step spectral preconditioner is constructed by combining the spectral preconditioner and sparse approximate inverse (SAI) preconditioner to speed up the convergence rate of iterative methods. Numerical experiments for scattering from conducting objects above or embeded in a lossy half-space are given to demonstrate the efficiency of the proposed method.

Citation:
D.-Z. Ding, R.-S. Chen, and Z. Fan, "Application of two-step spectral preconditioning technique for electromagnetic scattering in a half space," Progress In Electromagnetics Research, Vol. 94, 383-402, 2009.
doi:10.2528/PIER09060906
http://www.jpier.org/PIER/pier.php?paper=09060906

References:
1. Geng, N., A. Sullivan, and L. Carin, "Multilevel fastmultipole algorithm for scattering from conducting targets above or embedded in a lossy half space," IEEE Trans. Geosci. Remote v, Vol. 38, No. 4, 1561-1573, 2000.
doi:10.1109/36.851956

2. Liu, Z. J., J. Q. He, Y. J. Xie, A. Sullivan, and L. Carin, "Multi-level fast multipole algorithm for general targets on a half-space interface," IEEE Trans. Antennas Propagat., Vol. 50, No. 12, 1839-1849, 2002.

3. Li, L., J. Q. He, Z. J. Liu, X. L. Dong, and L. Carin, "MLFMA analysis of scattering from multiple targets in the presence of a half-space," IEEE Trans. Antennas Propagat., Vol. 51, No. 4, 810-819, 2003.
doi:10.1109/TAP.2003.811084

4. Geng, N., A. Sullivan, and L. Carin, "Fast multipole method for scatering from an arbitrary PEC target above or buried in a lossy half space," IEEE Trans. Antennas Propagat., Vol. 49, No. 5, 740-748, 2001.
doi:10.1109/8.929628

5. Harrington, R. F., "Field Computation by Moment Methods," R. E. Krieger, 1968.

6. 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

7. Chew, W. C., J. M. Jin, E. Midielssen, and J. M. Song, Fast and E±cient Algorithms in Computational Electromagnetics, Artech House, Boston , MA, 2001.

8. Shubair, R. M. and Y. L. Chow, "A simle and accurate complex image interpretation of vertical antennas present in contiguous dielectric halfspaces," IEEE Trans. Antennas Propagat., Vol. 41, 806-812, 1993.
doi:10.1109/8.250457

9. Aksun, M. I., "A robust approach for the derivation of closed-form Green's functions," IEEE Trans. Microw. Theory Tech., Vol. 44, 651-658, 1996.
doi:10.1109/22.493917

10. Geng, N., A. Sullivan, and L. Carin, "Fast multipole method for scattering from 3D PEC targets situated in a half-space environment," Microwave and Optical Technology Letters, Vol. 21, 399-405, 1999.
doi:10.1002/(SICI)1098-2760(19990620)21:6<399::AID-MOP3>3.0.CO;2-Z

11. Chew, W. C., et al., "Integral equation solvers for real world applications --- Some challenge problems," Proceedings of IEEE International Symposium on Antennas and Propagat., 91-93, Albuquerque, NM, 2006.

12. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat., Vol. 45, No. 10, 1488-1493, 1997.
doi:10.1109/8.633855

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

14. Chow, E. and Y. Saad, "Experimental study of ILU preconditioners for indefinite matrices," Journal of Computational and Applied Mathematics, Vol. 86, 387-414, 1997.
doi:10.1016/S0377-0427(97)00171-4

15. Carpentieri, B., I. S. Duff, L. Griud, and G. Alleon, "Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations," SIAM Journal on Scientific Computing, Vol. 27, No. 3, 774-792, 2005.
doi:10.1137/040603917

16. Malas, T. and L. Gurel, "Accelerating the multilevel fast multipole algorithm with the sparse-approximate-inverse (SAI)," SIAM Journal on Scientific Computing, Vol. 31, No. 3, 1968-1984, 2009.
doi:10.1137/070711098

17. Andriulli, F. P., K. Cools, H. Bagci, F. Olyslager, A. Buffa, S. Christiansen, and E. Michielssen, "A Multiplicative calderon preconditioner for the electric field integral equation," IEEE Trans. Antenna Propagat., Vol. 56, No. 8, 2398-2412, 2008.
doi:10.1109/TAP.2008.926788

18. Carpentieri, B., I. S. Duff, and L. Griud, "Sparse pattern selection strategies for robust frobenius-norm minimization preconditioners in electromagnetism," Numerical Linear Algebra Applications, Vol. 7--8, No. 7--8, 667-685, 2000.
doi:10.1002/1099-1506(200010/12)7:7/8<667::AID-NLA218>3.0.CO;2-X

19. Ding, D.-Z., R. S. Chen, and Z. H. Fan, "An e±cient sai preconditioning technique for higher order hierarchical MLFMM implementation," Progress In Electromagnetics Research, Vol. 88, 255-273, 2008.
doi:10.2528/PIER08111501

20. Erhel, J., K. Burrage, and B. Pohl, "Restarted GMRES preconditioned by deflation," Journal of Computational and Applied Mathematics, Vol. 69, 303-318, 1996.
doi:10.1016/0377-0427(95)00047-X

21. Rui, P. L., R. S. Chen, D. X. Wang, and E. K. N. Yung, "Spectral two-step preconditioning of multilevel fast multipole algorithm for the fast monostatic RCS calculation," IEEE Trans. Antennas Propagat., Vol. 55, No. 8, 2007.
doi:10.1109/TAP.2007.901853

22. Ding, D. Z., R. S. Chen, Z. H. Fan, and P. L. Rui, "A novel hierarchical two-level spectral preconditioning technique for multilevel fast multipole analysis of electromagnetic wave scattering," IEEE Trans. Antennas Propagat., Vol. 56, No. 4, 1122-1132, 2008.
doi:10.1109/TAP.2008.919188

24. Lindell, I. V., "Methods for Electromagnetic Field Analysis," IEEE Press, 1995.

25. Saad, Y., "Iterative Methods for Sparse Linear Systems," PWS Publishing Company, 1996.

26. Van Der Vorst, H. A. and C. Vuik, "The superlinear convergence behaviour of GMRES," Journal of Computational and Applied Mathematics, Vol. 48, 327-341, 1993.
doi:10.1016/0377-0427(93)90028-A

27. Lehoucq, R. B., D. C. Sorensen, and C. Yang, "ARPACK User's guide: Solution of large-scale problem with implicitly restart Arnoldi methods," SIAM, Philadelphia, 1998.

28. Morgan, R. B., "GMRES with deflated restarting," SIAM Journal of Scientific Computing, Vol. 24, 20-37, 2002.
doi:10.1137/S1064827599364659

29. Bağcı, H., A. E. Y³lmaz, V. Lomakin, and E. Michielssen, "Fast solution of mixed-potential time-domain integral equations for half-space environments," IEEE Trans. Geosci. Remote Sensing, Vol. 43, No. 2, 269-279, 2005.
doi:10.1109/TGRS.2004.841489

30. Geng, N. and L. Carin, "Fast multipole method for targets above or buried in lossy soil," IEEE Antennas and Propagat. Society International Symposium, 644-647, 1999.


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