PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 119 > pp. 85-105

TAYLOR-ORTHOGONAL BASIS FUNCTIONS FOR THE DISCRETIZATION IN METHOD OF MOMENTS OF SECOND KIND INTEGRAL EQUATIONS IN THE SCATTERING ANALYSIS OF PERFECTLY CONDUCTING OR DIELECTRIC OBJECTS (Invited Paper)

By E. Ubeda, J. M. Tamayo, and J. M. Rius

Full Article PDF (362 KB)

Abstract:
We present new implementations in Method of Moments of two types of second kind integral equations: (i) the recently proposed Electric-Magnetic Field Integral Equation (EMFIE), for perfectly conducting objects, and (ii) the Müller formulation, for homogeneous or piecewise homogeneous dielectric objects. We adopt the Taylor-orthogonal basis functions, a recently presented set of facet-oriented basis functions, which, as we show in this paper, arise from the Taylor's expansion of the current at the centroid of the discretization triangles. We show that the Taylor-orthogonal discretization of the EMFIE mitigates the discrepancy in the computed Radar Cross Section observed in conventional divergence-conforming implementations for moderately small, perfectly conducting, sharp-edged objects. Furthermore, we show that the Taylor-discretization of the Müller-formulation represents a valid option for the analysis of sharp-edged homogenous dielectrics, especially with low dielectric contrasts, when compared with other RWG-discretized implementations for dielectrics. Since the divergence-Taylor Orthogonal basis functions are facet-oriented, they appear better suited than other, edge-oriented, discretization schemes for the analysis of piecewise homogenous objects since they simplify notably the discretization at the junctions arising from the intersection of several dielectric regions.

Citation:
E. Ubeda, J. M. Tamayo, and J. M. Rius, "Taylor-Orthogonal Basis Functions for the Discretization in Method of Moments of Second Kind Integral Equations in the Scattering Analysis of Perfectly Conducting or Dielectric Objects (Invited Paper)," Progress In Electromagnetics Research, Vol. 119, 85-105, 2011.
doi:10.2528/PIER11051715
http://www.jpier.org/PIER/pier.php?paper=11051715

References:
1. Hodges, R. E. and Y. Rahmat-Samii, "The evaluation of MFIE integrals with the use of vector triangle basis functions," Microwave and Optical Technology Letters, Vol. 14, No. 1, 9-14, Jan. 1997.
doi:10.1002/(SICI)1098-2760(199701)14:1<9::AID-MOP4>3.0.CO;2-P

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

3. Rius, J. M., E. Ubeda, and J. Parrón, "On the testing of the magnetic field integral equation with RWG basis functions in method of moments," IEEE Transactions on Antennas and Propagation, Vol. 49, No. 11, 1550-1553, Nov. 2001.
doi:10.1109/8.964090

4. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 3, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818

5. Wilton, D. R., J. E. Wheeler, and III, "Comparison of convergence rates of the conjugate gradient method applied to various integral equation formulations," Progress In Electromagnetics Research, Vol. 5, 131-158, 1991.

6. Ubeda, E. and J. M. Rius, "MFIE MoM-formulation with curl-conforming basis functions and accurate Kernel-integration in the analysis of perfectly conducting sharp-edged objects," Microwave and Optical Technology Letters, Vol. 44, No. 4, Feb. 2005.
doi:10.1002/mop.20633

7. Ergül, Ö. and L. Gürel, "The use of curl-conforming basis functions for the magnetic-field integral equation," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 7, 1917-1926, Jul. 2006.
doi:10.1109/TAP.2006.877159

8. Ubeda, E. and J. M. Rius, "Comments on ``The use of curl-conforming basis functions for the magnetic-field integral equation"," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 7, 2142, Jul. 2008.
doi:10.1109/TAP.2008.924777

9. Ergül, Ö. and L. Gürel, "Improving the accuracy of the magnetic field integral equation with the linear-linear basis functions," Radio Science, Vol. 41, 2006, RS4004, doi:10.1029/2005RS003307.

10. Ubeda, E. and J. M. Rius, "Novel monopolar MoM-MFIE discretization for the scattering analysis of small objects," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 1, 50-57, Jan. 2006.
doi:10.1109/TAP.2005.861529

11. Müller, C., Foundations of the Mathematical Theory of Electromagnetic Waves, Springer, Berlin, Germany, 1969.

12. Chao, J. C., Y. J. Liu, F. J. Rizzo, P. A. Martin, and L. Udpa, "Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 12, 1416-1422, Dec. 1995.
doi:10.1109/8.475931

13. Ylä-Oijala, P. and M. Taskinen, "Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 12, Dec. 1995.
doi:10.1109/8.475931

14. Ylä-Oijala, P, M. Taskinen, and S. JÄarvenpää, "Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods ," Radio Science, Vol. 40, No. 6, RS6002, Nov. 2005.

15. Poggio, A. J. and E. K. Miller, "Integral equation solutions of threedimensional scattering problems," Computer Techniques for Electromagnetics, Vol. 4, R. Mittra, Ed., Pergamon Press, Oxford, UK, 1973.

16. Wu, T. K. and L. L. Tsai, "Scattering from arbitrarily-shaped lossy dielectric bodies of revolution," Radio Science, Vol. 12, 709-718, Sep.-Oct. 1977.

17. Chang, Y. and R. F. Harrington, "A surface formulation for characteristic modes of material bodies," IEEE Transactions on Antennas and Propagation, Vol. 25, 789-795, Nov. 1977.
doi:10.1109/TAP.1977.1141685

18. Ubeda, E., J. M. Tamayo, and J. M. Rius, "Orthogonal basis functions for the discretization of the magnetic-field integral equation in the low frequency regime," European Conference on Antennas and Propagation (EUCAP), Barcelona, Apr. 12-16, 2010.

19. Ubeda, E. and J. M. Rius, "New electric-magnetic field integral equation for the scattering analysis of perfectly conducting sharp-edged objects at very low or extremely low frequencies ," IEEE International Symposium on Antennas and Propagation, Toronto, Jul. 11-17, 2010.

20. Wu, W., A. W. Glisson, and D. Kajfez, "A study of two numerical procedures for the electric field integral equation at low frequency," Appl. Computat. Electromagn. Soc. J., Vol. 10, No. 3, Nov. 1995.

21. Lee, J., R. Lee, and R. J. Burkholder, "Loop star basis functions and a robust preconditioner for EFIE scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 51, No. 8, Aug. 2003.
doi:10.1109/TAP.2003.814736

22. Trintinalia, L. C. and H. Ling, "First order triangular patch basis functions for electromagnetic scattering analysis," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 11, 1521-1537, 2001.
doi:10.1163/156939301X00085

23. Van Bladel, J., Singular Electromagnetic Fields and Sources, Clarendon Press, Oxford, 1991.

24. Ubeda, E. and J. M. Rius, "Monopolar divergence-conforming and curl-conforming low-order basis functions for the electromagnetic scattering analysis," Microwave and Optical Technology Letters, Vol. 46, No. 3, 237-241, Aug. 2005.
doi:10.1002/mop.20955

25. Taskinen, M., "Electromagnetic surface integral equations and fully orthogonal higher order basis functions ," IEEE International Symposium on Antennas and Propagation, San Diego, Jul. 5-12, 2008.

26. Graglia, R. D., "On the numerical integration of the linear shape functions times the 3D's Green's function or its gradient on a plane triangle," IEEE Transactions on Antennas and Propagation, Vol. 41, No. 10, 1448-1455, Oct. 1993.
doi:10.1109/8.247786

27. Wilton, D. R., S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Transactions on Antennas and Propagation, Vol. 32, No. 3, 276-281, Mar. 1984.
doi:10.1109/TAP.1984.1143304

28. Ylä-Oijala, P., M. Taskinen, and J. Sarvas, "Surface integral equation method for general composite metallic and dielectric structures with junctions," Progress In Electromagnetics Research, Vol. 52, 81-108, 2005.
doi:10.2528/PIER04071301


© Copyright 2014 EMW Publishing. All Rights Reserved