Vol. 126
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]
2012-03-08
An Efficient High Order Multilevel Fast Multipole Algorithm for Electromagnetic Scattering Analysis
By
Progress In Electromagnetics Research, Vol. 126, 85-100, 2012
Abstract
An efficient higher order MLFMA is developed by using an ``extended-tree''. With this extended-tree, the size of the box at the finest level is reduced, and the cost associated with the aggregation and disaggregation operations is significantly decreased. The sparse approximate inverse (SAI) preconditioner is utilized to accelerate the convergence of iterative solutions. The Cholesky factorization, instead of the often used QR factorization, is employed to construct the SAI preconditioner for cavity scattering analysis, by taking advantage of the symmetry of the matrix arising from electric field integral equation. Numerical experiments show that the higher order MLFMA is more efficient than its low-order counterpart.
Citation
Xiao-Min Pan, Lu Cai, and Xin-Qing Sheng, "An Efficient High Order Multilevel Fast Multipole Algorithm for Electromagnetic Scattering Analysis," Progress In Electromagnetics Research, Vol. 126, 85-100, 2012.
doi:10.2528/PIER12020203
References

1. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, Piscataway, NJ, 1998.

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

3. Kolundzija, B. M. and B. D. Popovic, "Entire-domain Galerkin method for analysis of metallic antennas and scatterers," IEE Proceedings - H, Vol. 140, No. 1, 1-10, Feb. 1993.

4. Donepudi, K. C., "A novel implementation of multilevel fast multipole algorithm for higher order Galerkin's method," IEEE Trans. Antennas Propag., Vol. 48, 1192-1197, Aug. 2000.

5. Donepudi, K. C., J. M. Jin, S. Velamparambil, J. Song, and W. C. Chew, "A higher order parallelized multilevel fast multipole algorithm for 3-D scattering," IEEE Trans. Antennas Propag., Vol. 49, No. 7, 1069-1078, Jul. 2001.
doi:10.1109/8.933487

6. Notaros, B. M., "Higher order frequency-domain computational electromagnetics," IEEE Trans. Antennas Propag., Vol. 56, No. 8, 2251-2276, Aug. 2008.
doi:10.1109/TAP.2008.926784

7. Liu, Z.-L. and J. Yang, "Analysis of electromagnetic scattering with higher-order moment method and NURBS model," Progress In Electromagnetics Research, Vol. 96, 83-100, 2009.
doi:10.2528/PIER09071704

8. Eibert, T. F., Ismatullah, E. Kaliyaperumal, and C. H. Schmidt, "Inverse equivalent surface current method with hierarchical higher order basis functions, full probe correction and multi-level fast multipole acceleration," Progress In Electromagnetics Research, Vol. 106, 377-394, 2010.
doi:10.2528/PIER10061604

9. Zhang, H.-W., X.-W. Zhao, Y. Zhang, D. Garcia-Donoro, W.-X. Zhao, and C.-H. Liang, "Analysis of a large scale narrow-wall slotted waveguide array by parallel MoM out-of-core solver using the higher order basis functions," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 14-15, 1953-1965, 2010.

10. Lai, B., H.-B. Yuan, and C.-H. Liang, "Analysis of nurbs surfaces modeled geometries with higher-order MoM based aim," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 5-6, 683-691, 2011.
doi:10.1163/156939311794827285

11. Klopf, E. M., S. B. Manic, M. M. Ilic, and B. M. Notaros, "Efficient time-domain analysis of waveguide discontinuities using higher order FEM in frequency domain," Progress In Electromagnetics Research, Vol. 120, 215-234, 2011.

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 Propag., Vol. 45, No. 10, 1488-1493, Oct. 1997.
doi:10.1109/8.633855

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

14. Lee, J., J. Zhang, and C. C. Lu, "Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetics," IEEE Trans. Antennas Propag., Vol. 52, No. 9, 2277-2287, Sep. 2004.
doi:10.1109/TAP.2004.834084

15. Carpentieri, B., I. S. Duff, L. Griud, and G. Sylvand, "Combing fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations," SIAM J. Sci. Comput. , Vol. 27, No. 3, 774-792, 2005.
doi:10.1137/040603917

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

17. Malas, T. and L. Guirel, "Incomplete LU preconditioning with the multilevel fast multipole algorithm for electromagnetic scattering," SIAM J. Sci. Comput., Vol. 29, No. 4, 1476-1494, 2007.
doi:10.1137/060659107

18. 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

19. Pan, X. M. and X. Q. Sheng, "A sophisticated parallel MLFMA for scattering by extremely large targets," IEEE Antennas Propag. Mag., Vol. 50, No. 3, 129-138, Jun. 2008.
doi:10.1109/MAP.2008.4563583

20. Chow, E., "Parallel implementation and practical use of sparse approximate inverse preconditioners with a priori sparsity patterns," Intl. J. High Perf. Comput. Appl., Vol. 15, No. 1, 56-74, Feb. 2001.
doi:10.1177/109434200101500106