volume | PIER Journals

Abstract

This paper proposes a multilevel Green's function interpolation method (MLGFIM) to solve electromagnetic scattering from objects comprising both conductor and bi-isotropic objects using volume/surface integral equation (VSIE). Based on equivalence principle, the volume integral equation (VIE) in terms of volume electric and magnetic flux densities and surface integral equation (SIE) in terms of surface electric current density are first formulated for inhomogeneous bi-isotropic and conducting objects, respectively, and then are discretized using the method of moments (MoM). The MLGFIM is adopted to speed up the iterative solution of the resultant equation and reduces the memory requirement. Numerical examples are presented to show good accuracy and versatility of the proposed algorithm in dealing with a wide array of scattering problems.

1. Lindell, I. V., A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-isotropic Media, Artech House, Norwood, MA, 1994.

2. Serdyukov, A., I. Semchenko, S. Treyakov, and A. Sihvola, "Electromagnetics of Bi-anisotropic Materials Theory and Applications," Gordon and Breach Science Publishers, Amsterdam, 2001. Google Scholar

3. Bohren, C. F., "Light scattering by an optically active sphere," Chem. Phys. Lett., Vol. 29, 458-462, 1974. Google Scholar

4. Bohren, C. F., "Scattering of electromagnetic waves by an optically active cylinder," J. Colloid Interface Sci., Vol. 66, 105-109, 1978. Google Scholar

5. Worasawate, D., J. R. Mautz, and E. Arvas, "Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body," IEEE Trans. Antennas Propagat., Vol. 51, 1077-1084, 2003. Google Scholar

6. Wang, D. X., E. K. N. Yung, R. S. Chen, and P. Y. Lau, "An efficient volume integral equation solution to EM scattering by complex bodies with inhomogeneous bi-isotropy," IEEE Trans. Antennas Propagat., Vol. 55, 1970-1980, 2007. Google Scholar

7. Semichaevsky, A., A. Akyurtlu, D. Kem, D. H. Werner, and M. G. Bray, "Novel BI-FDTD approach for the analysis of chiral cylinders and spheres," IEEE Trans. Antennas Propagat., Vol. 54, 925-932, 2006. Google Scholar

8. Akyurtlu, A. and D. H. Werner, "A novel dispersive FDTD formulation for modeling transient propagation in chiral metamaterials," IEEE Trans. Antennas Propagat., Vol. 52, 2267-2276, 2004. Google Scholar

9. Sharma, R. and N. Balakrishnan, "Scattering of electromagnetic waves from arbitrary shaped bodies coated with a chiral material," Smart Mater. Struct., Vol. 7, 851-866, 1998. Google Scholar

10. Ghaffar, A. and Q. A. Naqvi, "Study of focusing of field refracted by a cylindrical plano-convex lens into a uniaxial crystal using Maslov's method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 5-6, 665-679, 2008. Google Scholar

11. Lu, C. C. and W. C. Chew, "A multilevel algorithm for solving a boundary integral equation of wave scattering," Microw. Opt. Tech. Lett., Vol. 7, 456-461, 1994. Google Scholar

12. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast ltipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propagat., Vol. 45, 1488-1493, 1997. Google Scholar

13. Yang, M. L. and X. Q. Sheng, "Parallel high-order FE-BI-MLFMA for scattering by large and deep coated cavities loaded with obstacles," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 13, 1813-1823, 2009. Google Scholar

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

15. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems," Radio Sci., Vol. 31, 1225-1251, 1996. Google Scholar

16. Ling, F., C. F. Wang, and J. M. Jin, "An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex image method," IEEE Trans. Microw. Theory Tech., Vol. 48, 832-837, 2000. Google Scholar

17. Hu, L., L. W. Li, and T.-S. Yeo, "Analysis of scattering by large inhomogeneous bi-anisotropic objects using AIM," Progress In Electromagnetics Research, Vol. 99, 21-36, 2009. Google Scholar

18. Chan, C. H., C. M. Lin, L. Tsang, and Y. F. Leung, "A sparse-matrix/canonical grid method for analyzing microstrip structures," IEICE Trans. Electron, E80-C, 1354{1359, 1997. Google Scholar

19. Li, S. Q., Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, "A sparse-matrix/canonical grid method for analyzing densely packed interconnects," IEEE Trans. Microw. Theory Tech., Vol. 49, 1221-1228, 2001. Google Scholar

20. Phillips, J. R. and J. K. White, "A precorrected-FFT method for electrostatic analysis of complicated 3-D structures," IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., Vol. 16, 1059-1072, 1997. Google Scholar

21. Nie, X. C., N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, "A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects," IEEE Trans. Antennas Propagat., Vol. 52, 818-824, 2005. Google Scholar

22. Wang, H. G., C. H. Chan, and L. Tsang, "A new multilevel Green's function interpolation method for large-scale low-frequency EM simulations," IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., Vol. 24, 1427-1443, 2005. Google Scholar

23. Wang, H. G. and C. H. Chan, "The implementation of multilevel Green's function interpolation method for full-wave electromagnetic problems ," IEEE Trans. Antennas Propagat., Vol. 55, 1348-1358, 2007. Google Scholar

24. Li, L., H. G. Wang, and C. H. Chan, "An improved multilevel Green's function interpolation method with adaptive phase compensation for large-scale full-wave EM simulation," IEEE Trans. Antennas Propagat., Vol. 56, 1381-1393, 2008. Google Scholar

25. Shi, Y., H. G. Wang, L. Li, and C. H. Chan, "Multilevel Green's function interpolation method for scattering from composite metallic and dielectric objects," J. Opt. Soc. Am. A, Vol. 25, 2535-2548, 2008. Google Scholar

26. Shi, Y. and C. H. Chan, "Multilevel Green's function interpolation method for analysis of 3-D frequency selective structures using volume/surface integral equation," J. Opt. Soc. Am. A, Vol. 27, 308-318, 2010. Google Scholar

27. Shi, Y. and C. H. Chan, "Solution to electromagnetic scattering by Bi-isotropic media using multilevel Green's function interpolation method," Progress In Electromagnetics Research, Vol. 97, 259-274, 2009. Google Scholar

28. Graglia, R. D., D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antennas Propagat., Vol. 45, 329-342, 1997. Google Scholar

29. Saad, Y. and M. Schultz, "GMRES: A generalized minimal residual algorithm for solving non symmetric linear systems," SIAM J. Sci. Stat. Comput., Vol. 7, 856-869, 1986. Google Scholar

30. Horn, R. A. and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, New York, 1991.

31. Xie, Y., J. He, A. Sullivan, and L. Carin, "A simple preconditioner for electric-field integral equations," Microw. Opt. Technol. Lett., Vol. 30, 51-54. Google Scholar

Prof. Yan Shi

Dr. Xiao Luan

Dr. Jun Qin

Dr. Chaojie Lv

Professor Chang-Hong Liang