Vol. 106
Latest Volume
All Volumes
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]
2010-07-28
Inverse Equivalent Surface Current Method with Hierarchical Higher Order Basis Functions, Full Probe Correction and Multilevel Fast Multipole Acceleration (Invited Paper)
By
Progress In Electromagnetics Research, Vol. 106, 377-394, 2010
Abstract
An inverse equivalent surface current method working with equivalent electric and/or magnetic surface current densities on appropriately chosen Huygens surfaces is investigated. The considered model with triangular surface meshes is compatible with the models known from method of moments (MoM) solutions of surface integral equations. Divergence conforming current basis functions of order 0.5 and of order 1.5 are considered, where the order 0.5 functions are the well-known Rao-Wilton-Glisson basis functions. Known near-field samples typically obtained from measurements are mapped on the unknown equivalent surface current densities utilizing the radiation integrals of the currents as forward operator, where the measurement probe influence is formulated in a MoM like weighting integral. The evaluation of the forward operator is accelerated by adaptation of the multilevel fast multipole method (MLFMM) to the inverse formulation, where the MLFMM representation is the key to full probe correction by employing only the far-field patterns of the measurement probe antennas. The resulting fully probe corrected algorithm is very flexible and efficient, where it is found that the computation speed is mostly dependent on the MLFMM configuration of the problem and not that much on the particular equivalent current expansion as long as the expansion is able to represent the currents sufficiently well. Inverse current and far-field pattern results are shown for a variety of problems, where near-field samples obtained from simulations as well as from realistic measurements are considered.
Citation
Thomas F. Eibert, Ismatullah, E. Kaliyaperumal, and Carsten H. Schmidt, "Inverse Equivalent Surface Current Method with Hierarchical Higher Order Basis Functions, Full Probe Correction and Multilevel Fast Multipole Acceleration (Invited Paper)," Progress In Electromagnetics Research, Vol. 106, 377-394, 2010.
doi:10.2528/PIER10061604
References

1. Yaghjian, A., "An overview of near-field antenna measurements," IEEE Trans. Antennas Propag., Vol. 34, No. 1, 30-45, 1986.

2. Hansen, J. E., Spherical Near-field Antenna Measurements, IEE Electromagnetic Wave Series 26, 1988.

3. Kerns, D. M., "Plane-wave scattering-matrix theory of antennas and antenna-antenna interactions," National Bureau of Standards, Boulder CO, 1981.

4. Cappellin, C., O. Breinbjerg, and A. Frandsen, "Properties of the transformation from the spherical wave expansion to the plane wave expansion," Radio Sci., Vol. 43, No. 1, 2008.

5. Sarkar, T. and A. Taaghol, "Near-field to near/far-field transformation for arbitrary near-field geometry utilizing an equivalent electric current and MoM," IEEE Trans. Antennas Propag., Vol. 47, No. 3, 566-573, 1999.

6. Alvarez, Y., F. Las-Heras, and M. R. Pino, "Reconstruction of equivalent currents distribution over arbitrary three-dimensional surfaces based on integral equation algorithms," IEEE Trans. Antennas Propag., Vol. 55, No. 12, 3460-3468, 2007.

7. Eibert, T. F. and C. H. Schmidt, "Multilevel fast multipole accelerated inverse equivalent current method employing Rao-Wilton-Glisson discretization of electric and magnetic surface currents," IEEE Trans. Antennas Propag., Vol. 57, No. 4, 1178-1185, 2009.

8. 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, 1982.

9. Petre, P. and T. K. Sarkar, "Planar near-field to far-field transformation using an equivalent magnetic current approach," IEEE Trans. Antennas Propag., Vol. 40, No. 11, 1348-1356, 1992.

10. Alvarez, Y., F. Las-Heras, M. R. Pino, and J. A. Lopez, "Acceleration of the sources reconstruction method via the fast multipole method," IEEE Antennas Propag. Intern. Symp., 2008.

11. Lopez, Y. A., F. Las-Heras, and M. R. Pino, "Application of the adaptive cross approximation algorithm to the sources reconstruction method," European Conf. Antennas Propag., 2009.

12. Eibert, T. F., "A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space integrals," IEEE Trans. Antennas Propag., Vol. 53, No. 2, 814-817, 2005.

13. Tzoulis, A. and T. F. Eibert, "Efficient electromagnetic near-field computation by the multilevel fast multipole method employing mixed near-field/far-field translations," IEEE Antennas Wireless Propag. Lett., Vol. 4, 449-452, 2005.

14. Chew, W. C., T. J. Cui, and J. M. Song, "A FAFFA-MLFMA algorithm for electromagnetic scattering," EEE Trans. Antennas Propag., Vol. 50, No. 11, 1641-1649, 2002.

15. Jorgensen, E., J. L. Volakis, P. Meincke, and O. Breinbjerg, "Higher order hierarchical Legendre basis functions for electromagnetic modeling," IEEE Trans. Antennas Propag., Vol. 52, No. 11, 2985-2995, 2004.

16. Sun, D. K., J. F. Lee, and Z. Cendes, "Construction of nearly orthogonal Nedelec bases for rapid convergence with multilevel preconditioned solvers," SIAM J. Sci. Comput., Vol. 23, No. 4, 1053-1076, 2001.

17. Ismatullah and T. F. Eibert, "Surface integral equation solutions by hierarchical vector basis functions and spherical harmonics based multilevel fast multipole method," IEEE Trans. Antennas Propag., Vol. 57, No. 7, 2084-2093, 2009.

18. Schmidt, C. H., M. M. Leibfritz, and T. F. Eibert, "Fully probe-corrected near-field far-field transformation employing plane wave expansion and diagonal translation operators," IEEE Trans. Antennas Propag., Vol. 56, No. 3, 737-746, 2008.

19. Araque Quijano, J. L. and G. Vecchi, "Field and source equivalence in source reconstruction on 3D surfaces," Progress In Electromagnetics Reseach, Vol. 103, 67-100, 2010.

20. Chew, W. C., J.-M. Jin, and E. Michielssen, Fast and Effcient Algorithms in Computational Electromagnetics, Artech House, Boston, 2001.

21. Saad, Y., Iterative Methods for Sparse Linear Systems, PWS, Boston, 1996.

22. Bjorck, A., Numerical Methods for Least Squares Problems, SIAM, Philadelphia, 1996.

23. Las-Heras, F., B. Galocha, and J. L. Besada, "Equivalent source modelling and reconstruction for antenna measurement and synthesis," IEEE Antennas Propag. Intern. Symp., 2007.