Generalized method of moments: A framework for analyzing scattering from homogeneous dielectric bodies

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 28, Issue 3, 2011, Pages 328-340

  Nair, Naveen V ^a   Shanker, Balasubramaniam ^a,b  

^a Michigan State University   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

METHOD OF MOMENTS;

APPROXIMATION FUNCTION; BASIS FUNCTIONS; CONTINUITY CONSTRAINTS; DIELECTRIC BODY; DIFFERENT ORDER; GENERALIZED METHOD OF MOMENTS; HELMHOLTZ; HIGHER ORDER; HOMOGENEOUS DIELECTRICS; NUMERICAL EXPERIMENTS; POGGIO-MILLER-CHANG-HARRINGTON-WU-TSAI; RAO-WILTON-GLISSON BASIS FUNCTIONS; SPATIAL VARIATIONS;

INTEGRAL EQUATIONS;

EID: 79952329665     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.28.000328     Document Type: Article

References (31)

1. I.-T. Chiang and W. C. Chew, "A coupled PEC-TDS surface integral equation approach for electromagnetic scattering and radiation from composite metallic and thin dielectric objects," IEEE Trans. Antennas Propagat. 54, 3511-3516 (2006). (Pubitemid 44824301)
2. W. R. Stone, Radar Cross Section of Complex Targets (IEEE, 1999).
3. L. I. Goray, "Numerical analysis of the efficiency of multilayercoated gratings using integral method," Nuclear Inst. Meth. Phys. Res. A 536, 211-221 (2005).
4. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).
5. P. H. Siegel, "Terahertz technology," IEEE Trans. Microwave Theory Tech. 50, 910-928 (2002). (Pubitemid 34255210)
6. L. N. Medgyesi-Mitschang, J. M. Putnam, and M. B. Gedera, "Generalized method of moments for three-dimensional penetrable scatterers," J. Opt. Soc. Am. A 11, 1383-1398 (1994).
7. P. Yla-Oijala and M. Taskinen, "Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects," IEEE Trans. Antennas Propag. 53, 3316-3323 (2005). (Pubitemid 41555334)
8. R. D. Graglia, D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antennas Propag. 45, 329-342 (1997). (Pubitemid 127770784)
9. R. Graglia and G. Lombardi, "Singular higher order complete vector bases for finite methods," IEEE Trans. Antennas Propag. 52, 1672-1685 (2004).
10. S. Chen, W. C. Chew, J. Song, and J.-S. Zhao, "Analysis of low frequency scattering from penetrable scatterers," IEEE Trans. Geosci. Remote Sensing 39, 726-735 (2001). (Pubitemid 32432729)
11. S. Chen, J.-S. Zhao, and W. C. Chew, "Analyzing low-frequency electromagnetic scattering from a composite object," IEEE Trans. Geosci. Remote Sensing 40, 426-433 (2002). (Pubitemid 34505771)
12. Y. Chu, W. C. Chew, J. Zhao, and S. Chen, "A surface integral equation formulation for low-frequency scattering from a composite object," IEEE Trans. Antennas Propag. 51, 2837-2844 (2003).
13. S. Yan, J.-M. Jin, and Z. Nie, "A comparative study of different Calderón preconditioned PMCHWT formulations," in Antennas and Propagation Society International Symposium (APSURSI), 2010 (IEEE, 2010), pp. 1-4.
14. A. Bossavit, Computational Electromagnetism (Academic,1998).
15. I. Babuska and J. M. Melenek, "The partition of unity method," Int. J. Numer. Meth. Eng. 40, 727-858 (1997).
16. C. A. M. Duarte, I. Babuska, and J. T. Oden, "Generalized finite element methods for three-dimensional structural mechanics problems," Comput. Struct. 77, 215-232 (2000).
17. I. Babuska, U. Banerjee, and U. Osorn, "Meshless and generalized fem: a survey of some major results," in Meshfree Methods for Partial Differential Equations, M. Griebel and M. A. Sciweitzer, eds. (Springer Verlag, 2002).
18. L. Chuan and B. Shanker, "Generalized finite element method for vector electromagnetic problems," IEEE Trans. Antennas Propag. 55, 1369-1381 (2007). (Pubitemid 46805317)
19. R. F. Harrington, "Boundary integral formulations for homogeneous material bodies," J. Electromagn. Waves. Appl. 3, 1-15 (1989).
20. J. R. Mautz and R. F. Harrington, "Electromagnetic scattering from a homogeneous body of revolution," Arch. Elektr. Uebertrag. 33, 71-80 (1979).
21. C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer Verlag, 1969).
22. N. Nair and B. Shanker, "Generalized method of moments: a novel discretization scheme for integral equations," IEEE Trans. Antennas Propagat. to be published; technical report available at https://www.egr.msu. edu/ece/technical-papers (2010).
23. G. Vecchi, "Loop-star decomposition of basis functions in the discretization of the EFIE," IEEE Trans. Antennas Propag. 47, 339-346 (1999).
24. M. Khayat and D. Wilton, "Numerical evaluation of singular and near-singular potential integrals," IEEE Trans. Antennas Propag. 53, 3180-3190 (2005). (Pubitemid 41555317)
25. L. Knockaert, "A general Gauss theorem for evaluating singular integrals over polyhedral domains," Electromagnetics 11, 269-280 (1991). (Pubitemid 21682256)
26. S. Järvenpää, M. Taskinen, and P. Ylä-Oijala, "Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra," Int. J. Numer. Meth. Eng. 58, 1149-1165 (2003). (Pubitemid 37317279)
27. L. F. Canino, J. J. Ottusch, M. A. Stalzer, J. L. Visher, and S. M. Wandzura, "Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nystrom discretization," J. Comput. Phys. 146, 627-663 (1998). (Pubitemid 128180422)
28. M. Vikram and B. Shanker, "An incomplete review of fast multipole methods from static to wideband as applied to problems in computational electromagnetics," Appl. Comput. Electromag. Soc. J. 24, 79-108 (2009).
29. A. C. Woo, H. T. G. Wang, M. J. Schuh, and M. L. Sanders, "Benchmark radar targets for the validation of computational electromagnetics programs," IEEE Antennas Propag. Mag. 35, 84-89 (1993).
30. S.-C. Lee, M. N. Vouvakis, and J.-F. Lee, "A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays," J. Comput. Phys. 203, 1-21 (2005). (Pubitemid 40004126)
31. F. P. Andriulli, K. Cools, F. Olyslager, and E. Michielssen, "Time domain Calderón identities and their application to the integral equation analysis of scattering by PEC objects part II: stability," IEEE Trans. Antennas Propag. 57, 2365-2375 (2009).