Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By H.-G. Wang and C. H. Chan

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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: (See works that cites this article)
H.-G. Wang and C. H. Chan, "Mixture Effective Permittivity Simulations Using Imlmqrf Method on Preconditioned EFIE," Progress In Electromagnetics Research, Vol. 57, 285-310, 2006.

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.

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.

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.

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.

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.

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.

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.

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

17. Whites, K. W., 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.

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.

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.

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.

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.

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