Vol. 82
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] 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]
2008-03-01
Schwarz-Krylov Subspace Method for MLFMM Analysis of Electromagnetic Wave Scattering Problems
By
Progress In Electromagnetics Research, Vol. 82, 51-63, 2008
Abstract
In this paper, the high-order hierarchical basis functions are used for solving electromagnetic wave scattering problems. The multilevel fast multipole method (MLFMM) is applied to accelerate the matrix-vector product operation and the Schwarz method is employed to speed up the convergence rate of the Krylov subspace iterative methods. The efficiency of the proposed approach is studied on several numerical model problems and the comparison with conventional Kryloviterativ e methods is made. Numerical results demonstrate that the combination of the Schwarz method and the Krylovsubspace iterative method is very effective with MLFMM and can reduce the overall simulation time significantly.
Citation
Ping-Liang Rui, Ru-Shan Chen, Zhiwei Liu, and Ya-Ning Gan, "Schwarz-Krylov Subspace Method for MLFMM Analysis of Electromagnetic Wave Scattering Problems," Progress In Electromagnetics Research, Vol. 82, 51-63, 2008.
doi:10.2528/PIER08013003
References

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

2. Hatamzadeh-Varmazyar, S., M. Naser-Moghadasi, and Z. Masouri, "A moment method simulation of electromagnetic scattering from conducting bodies," Progress In Electromagnetics Research, Vol. 81, 99-119, 2008.
doi:10.2528/PIER07122502

3. Wang, S., X. Guan, D.Wang, X. Ma, and Y. Su, "Electromagnetic scattering by mixed conducting/dielectric objects using higherorder MOM," Progress In Electromagnetics Research, Vol. 66, 51-63, 2006.
doi:10.2528/PIER06092101

4. Li, C. and Z. Shen, "Electromagnetic scattering by a conducting cylinder coated with metamaterials," Progress In Electromagnetics Research, Vol. 42, 91-105, 2003.
doi:10.2528/PIER03012901

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

6. Donepudi, K. C., J. M. Song, J. M. Jin, et al. "A novel implementation of multilevel fast multipole algorithm for higher order galerkin method," IEEE Trans. Antennas and Propagat., Vol. 48, No. 8, 1192-1197, Aug. 2000.
doi:10.1109/8.884486

7. Kang, G., J. M. Song, and W. C. Chew, "A novel grid-robust higher-order vector basis functions for the method of moments," IEEE Trans. Antennas and Propagat., Vol. 49, No. 6, 908-915, June 2001.
doi:10.1109/8.931148

8. Andersen, L. S. and J. L. Volakis, "Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics," IEEE Trans. Antennas and Propagat., Vol. 47, No. 1, 112-120, Jan. 1999.
doi:10.1109/8.753001

9. Webb, J. P., "Hierarchical vector basis functions of arbitrary order for triangular and tetrahedral finite elements," IEEE Trans. Antennas and Propagat., Vol. 47, No. 8, 1244-1253, Aug. 1999.
doi:10.1109/8.791939

10. Chew, W. C., J. M. Jin, E. Midielssen, and J.M. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001.

11. Zhao, X. W., C.-H. Liang, and L. Liang, "Multilevel fast multipole algorithm for radiation characteristics of shipborne antennas above seawater," Progress In Electromagnetics Research, Vol. 81, 291-302, 2008.
doi:10.2528/PIER08012003

12. Zhang, Y. J. and E. P. Li, "Fast multipole accelerated scattering matrix method for multiple scattering of a large number of cylinders," Progress In Electromagnetics Research, Vol. 72, 105-126, 2007.
doi:10.2528/PIER07030503

13. Wan, J. X., T. M. Xiang, and C.-H. Liang, "The fast multipole algorithm for analysis of large-scale microstrip antenna arrays," Progress In Electromagnetics Research, Vol. 49, 239-255, 2004.
doi:10.2528/PIER04042201

14. Pan, Y. C. and W. C. Chew, "A fast multipole method for embedded structure in a stratified medium," Progress In Electromagnetics Research, Vol. 44, 1-38, 2004.
doi:10.2528/PIER03050602

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

16. Sertel, K. and J. L. Volakis, "Incomplete LU preconditioner for FMM implementation," Micro. Opt. Tech. Lett., Vol. 26, No. 7, 265-267, 2000.
doi:10.1002/1098-2760(20000820)26:4<265::AID-MOP18>3.0.CO;2-O

17. Lee, J., C. C. Lu, and J. Zhang, "Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems," J. Comput. Phy., Vol. 185, 158-175, 2003.
doi:10.1016/S0021-9991(02)00052-9

18. Chow, E. and Y. Saad, "Experimental study of ILU preconditioners for indefinite matrices," J. Comput. Appl. Math., Vol. 86, No. 2, 387-414, 1997.
doi:10.1016/S0377-0427(97)00171-4

19. Schwarz, H. A., Gesammelte Mathematische Abhandlungen, Vol. 2, 133-143, Springer-Verlag, 1890.

20. Saad, Y., Iterative Methods for Sparse Linear Systems, PWS Publishing Company, 1995.

21. Woo, A. C., H. T. G. Wang, M. J. Schuh, and M. L. Sanders, "EM programmer’s notebook-benchmark radar targets for the validation of computational electromagnetics programs," IEEE Trans. Antennas and Propagat., Vol. 35, No. 1, 84-89, Feb. 1993.

22. Rui, P. L. and R. S. Chen, "An efficient sparse approximate inverse preconditioning for FMM implementation," Micro. Opt. Tech. Lett., Vol. 49, No. 7, 1746-1750, 2007.
doi:10.1002/mop.22538

23. Rui, P. L., S. S. Li, and R. S. Chen, "Application of SSOR preconditioned GMRESR algorithm for FEM analysis of Helmholtz equations," IEEE Int’l Symposium on Antennas and Propagation, 1173-1176, 2006.

24. Yuan, H. W., S. X. Gong, X. Wang, and W. T. Wang, "Scattering analysis of a printed dipole antenna using PBG structures," Progress In Electromagnetics Research B, Vol. 1, 189-195, 2008.
doi:10.2528/PIERB07102302

25. Varmazyar, S. H. and M. N. Moghadasi, "An integral equation modeling of electromagnetic scattering from the surfaces of arbitrary resistance distribution," Progress In Electromagnetics Research B, Vol. 3, 157-172, 2008.
doi:10.2528/PIERB07121404

26. Varmazyar, S. H. and M. N. Moghadasi, "New numerical method for determining the scattered electromagnetic fields from thin wires," Progress In Electromagnetics Research B, Vol. 3, 207-218, 2008.
doi:10.2528/PIERB07121303

27. Ho, M., "Scattering of electromagnetic waves from vibrating perfect surfaces: Simulation using relativistic boundary conditions," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 4, 425-433, 2006.
doi:10.1163/156939306776117108

28. Li, Y. L., J. Y. Huang, and M. J. Wang, "Scattering cross section for airborne and its application," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2341-2349, 2007.
doi:10.1163/156939307783134254

29. Zhong, X. J., T. J. Cui, Z. Li, Y. B. Tao, and H. Lin, "Terahertz-wave scattering by perfectly electrical conducting objects," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 15, 2331-2340, 2007.
doi:10.1163/156939307783134443

30. Bucci, O. M., G. Delia, and M. Santojanni, "A fast multipole approach to 2D scattering evaluation based on a non redundant implementation of the method of auxiliary sources," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1715-1725, 2006.
doi:10.1163/156939306779292174

31. 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