Vol. 57
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]
2005-09-27
Mixture Effective Permittivity Simulations Using Imlmqrf Method on Preconditioned EFIE
By
Progress In Electromagnetics Research, Vol. 57, 285-310, 2006
Abstract
Effective permittivity of mixtures of lossy dielectric are important quantities to be studied in microwave remote sensing of soil moisture, sea ice, dry and wet snow, in geophysical probing of properties of porous rocks and in composite materials. In this paper, these quantities are studied with large-scale numerical solutions of Maxwell equations in the electroquasistatic limit using fast electromagnetic algorithms. The preconditioned EFIE method instead of scalar potential scattering method for the simulation of the relative permittivity of the mixture with conducting particles in quasi-static environment is introduced. Furthermore, Algorithm IMLMQRF, which is kernel independent for quasi-static problems with a complexity of O(N log N), is implemented to accelerate the matrix-vector multiply when CG iteration is applying on this preconditioned EFIE system. Subsequently, numerical examples, viz., the permittivity extractions from two lattice structures and one random distribution structure with the unknowns from about 1,000 to 50,000 are efficiently simulated by our method in this paper. The numerical results demonstrate the efficiency of this hybrid method.
Citation
Hao-Gang Wang, and Chi Chan, "Mixture Effective Permittivity Simulations Using Imlmqrf Method on Preconditioned EFIE," Progress In Electromagnetics Research, Vol. 57, 285-310, 2006.
doi:10.2528/PIER05072603
References

1. Wang, J. R. and T. J. Schmugge, "An empirical model for the complex dielectric permittivity of soils as a function of water content," IEEE Trans. Geosci. Remote Sens., Vol. 18, 288-295, 1980.

2. Schmugge, T. J., "Effect of soil texture on the microwave emission from soils," IEEE Trans. Geosci. Rem. Sens., Vol. 18, 353-361, 1980.

3. Golden, K. M., "The interaction of microwave with sea ice," Wave Propagation in Complex Media, Vol. 96, 75-94, 1997.

4. Nghiem, S. V. et al., "Evolution in polarimetric signatures of thin saline ice under constant growth," Radio Sci., Vol. 32, No. 1, 127-151, 1997.
doi:10.1029/96RS03051

5. Perovich, D. K. and A. J. Gow, "A statistical description of the microstructure of young sea ice," J. Geophys. Res., Vol. 96, No. 16, 943-1695, 1991.

6. Linlor, W., "Permittivity and attenuation of wet snow between 4 and 12 GHz," J. Appl. Phys., Vol. 23, 2811-2816, 1980.
doi:10.1063/1.327947

7. Colbeck, S. C., "The geometry and permittivity of snow at high frequencies," J. Appl. Phys., Vol. 20, 45-61, 1982.

8. Hallikainen, M. T., F. T. Ulaby, and T. E. V. Deventer, "Extinction behavior of dry snow in the 18-90 GHz range," IEEE Trans. Geosci. Rem. Sens., Vol. 25, 737-750, 1987.

9. Chew, W. C., J. A. Friedrich, and R. Geiger, "A multiple scattering solution for the effective permittivity of a sphere mixture," IEEE Trans. Geosci. and Rem. Sens., Vol. 28, No. 2, 207-214, 1990.
doi:10.1109/36.46700

10. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves: Advanced Topics, John Wiley & Sons, 2001.

11. McPhedran, R. C. and D. R. McKenzie, "The conductivity of lattices of spheres I. The simple cubic lattice," Proceeding of the Royal Society, 45-63, 1978.

12. Doyle, W. T., "The Clausius-Mossotti problem for cubic arrays of spheres," Journal of Applied Physics, Vol. 49, 795-797, 1978.
doi:10.1063/1.324659

13. Kärkkäinen, K. K., A. H. Sihvola, and K. I. Nikoskinen, "Effective permittivity of mixtures: numerical validation by FDTD method," IEEE Trans. Geosci. Rem. Sens., Vol. 38, No. 3, 1303-1308, 2000.
doi:10.1109/36.843023

14. Kärkkäinen, K. K., A. H. Sihvola, and K. I. Nikoskinen, "Analysis of a three-dimensional dielectric mixture with finite difference method," IEEE Trans. Geosci. Rem. Sens., Vol. 39, No. 5, 1013-1018, 2001.
doi:10.1109/36.921419

15. Whites, K. W., "Permittivity of a multiphase and isotropic lattice of spheres at low frequency," Journal of Applied Physics, Vol. 88, No. 4, 1962-1970, 2000.
doi:10.1063/1.1305828

16. Wu, F. and and K. W. Whites, "Computation of static effective permittivity for a multiphase lattice of cylinders," Electromagnetics, Vol. 21.97-114, 97-114, 2001.
doi:10.1080/02726340151134380

17. Whites, K. W. and and F. Wu, "Effects of particle shape on the effective permittivity of composite materials with measurements for lattice cubes," IEEE Trans. Microwave Theory Tech., Vol. 50, No. 7, 1723-1729, 2002.
doi:10.1109/TMTT.2002.800422

18. Zhao, J. S. and W. C. Chew, "Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies," IEEE Trans. Antennas Propagat., Vol. 48, No. 10, 1635-1645, 2000.
doi:10.1109/8.899680

19. Wang, H. G., C. H. Chan, L. Tsang, and V. Jandhyala, "An improved multi-level matrix QR factorization for large-scale simulations on magnetoquasistatic analysis of integrated circuits over multi-layered lossy substrates," submit to IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems..

20. Even, S., Graph Algorithms, Computer Science Press, Rockville, 1979.

21. Graglia, R. D., D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antennas and Propagat., Vol. 45, No. 3, 329-342, 1997.
doi:10.1109/8.558649

22. Kapur, S. and D. E. Long, "IES3 : a fast integral equation solver for efficient 3-dimensional extraction," IEEE/ACM Int. Conf. Computer-Aided Design, No. 11, 448-455, 1997.

23. Kapur, S. and D. E. Long, "IES3 : efficient electrostatic and electromagnetic simulation," IEEE Trans. Computational Science and Engineering, Vol. 5, No. 12, 60-67, 1998.
doi:10.1109/99.735896

24. Golub, G. H. and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 1996.

25. Fischer, A. E., D. W. Eggert, and S. M. Ross, Applied C: An Introduction and More, McGraw-Hill, Boston, 2001.

26. Tsang, L., J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves Volume II, John Wiley & Sons, Inc., New York, 2001.

27. Press, W. H. et al., Numerical Recipes in C++, University Press, Cambridge, 2002.