Vol. 94
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2009-07-29
Application of Two-Step Spectral Preconditioning Technique for Electromagnetic Scattering in a Half Space
By
Progress In Electromagnetics Research, Vol. 94, 383-402, 2009
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
Da-Zhi Ding Ru-Shan Chen Zhenhong 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.