Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm

IEEE Transactions on Antennas and Propagation

Volumn 57, Issue 1, 2009, Pages 176-187

  Ergul, Özgür ^a   Gurel, Levent ^a  

^a BILKENT UNIVERSITY   (Turkey)

Author keywords

Dielectrics; Iterative solutions; Multilevel fast multipole algorithm (MLFMA); Surface integral equations

Indexed keywords

ALGORITHMS; INTEGRAL EQUATIONS;

COMBINED-FIELD INTEGRAL EQUATIONS; DIELECTRIC OBJECTS; DIELECTRICS; EQUATION FORMULATIONS; FIELD FORMULATIONS; ITERATIVE SOLUTIONS; MAGNETIC CURRENTS; MATRIX EQUATIONS; MULTILEVEL FAST MULTIPOLE ALGORITHM (MLFMA); RAO-WILTON-GLISSON FUNCTIONS; SCATTERING PROBLEMS; SURFACE INTEGRAL EQUATIONS;

DIELECTRIC MATERIALS;

EID: 63149142723     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2008.2009665     Document Type: Article

References (48)

1. A. J. Poggio and E. K. Miller, "Integral equation solutions of three-dimensional scattering problems," in Computer Techniques for Electromagnetics, R. Mittra, Ed. Oxford, U.K.: Pergamon Press, 1973, ch. 4.
2. R. F. Harrington, Field Computation by Moment Methods. New York: Macmillan, 1968.
3. C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves. New York: Springer, 1969.
4. T. K. Wu and L. L. Tsai, "Scattering from arbitrarily-shaped lossy dielectric bodies of revolution," Radio Sci., vol. 12, pp. 709-718, Sep.-Oct. 1977.
5. Y. Chang and R. F. Harrington, "A surface formulation for characteristic modes of material bodies," IEEE Trans. Antennas Propag., vol. AP-25, pp. 789-795, Nov. 1977.
6. J. R. Mautz and R. F. Harrington, "Electromagnetic scattering from a homogeneous material body of revolution," AEÜ, vol. 33, pp. 71-80, Feb. 1979.
7. R. F. Harrington, "Boundary integral formulations for homogeneous material bodies," J. Electromagn. Waves Applicat., vol. 3, no. 1, pp. 1-15, 1989.
8. S. M. Rao and D. R. Wilton, "E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies," Electromagn., vol. 10, no. 4, pp. 407-421, Oct.-Dec. 1990.
9. X.-Q. Sheng, J.-M. Jin, J. Song, W. C. Chew, and C.-C. Lu, "Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies," IEEE Trans. Antennas Propag., vol. 46, no. 11, pp. 1718-1726, Nov. 1998.
10. P. Ylä-Oijala, "Application of a novel CFIE for electromagnetic scattering by dielectric objects," Microw. Opt. Technol., vol. 35, no. 10, pp. 3-5, Oct. 2002.
11. T. W. Lloyd, J. M. Song, G. Kang, and C.-C. Lu, "Numerical study of surface integral formulations for homogeneous bodies," in Proc. IEEE Antennas and Propag. Soc. Int. Symp., 2004, pp. 3895-3898.
12. P. Ylä-Oijala and M. Taskinen, "Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects," IEEE Trans. Antennas Propag., vol. 53, no. 3, pp. 1168-1173, Mar. 2005.
13. P. Ylä-Oijala and M. Taskinen, "Well-conditioned Müller formulation for electromagnetic scattering by dielectric objects," IEEE Trans. Antennas Propag., vol. 53, no. 10, pp. 3316-3323, Oct. 2005.
14. P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, "Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods," Radio Sci., vol. 40, Nov. 2005, RS6002, doi:10.1029/2004RS003169.
15. T. W. Lloyd, J. M. Song, and M. Yang, "Numerical study of surface integral formulations for low-contrast objects," IEEE Antennas Wireless Propag. Lett., vol. 4, pp. 482-485, 2005.
16. P. Ylä-Oijala and M. Taskinen, "Improving conditioning of electromagnetic surface integral equations using normalized field quantities," IEEE Trans. Antennas Propag., vol. 55, no. 1, pp. 178-185, Jan. 2007.
17. J. Song, C.-C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag., vol. 45, no. 10, pp. 1488-1493, Oct. 1997.
18. P. Ylä-Oijala, M. Taskinen, and J. Sarvas, "Surface integral equation method for general integral equation method for general composite metallic and dielectric structures with junctions," Progress In Electromagn. Res. (PIER), vol. 52, pp. 81-108, 2005, doi:10.2528/PIER04071301.
19. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., vol. AP-30, no. 3, pp. 409-418, May 1982.
20. R. E. Hodges and Y. Rahmat-Samii, "The evaluation of MFIE integrals with the use of vector triangle basis functions," Microw. Opt. Technol. Lett., vol. 14, no. 1, pp. 9-14, Jan. 1997.
21. D. A. Dunavant, "High degree efficient symmetrical Gaussian quadrature rules for the triangle," Int. J. Numer. Meth. Eng., vol. 21, pp. 1129-1148, 1985.
22. L. Gürel and Ö. Ergül, "Singularity of the magnetic-field integral equation and its extraction," IEEE Antennas Wireless Propag. Lett., vol. 4, pp. 229-232, 2005.
23. Ö. Ergül, "Fast multipole method for the solution of electromagnetic scattering problems," M.S. thesis, Bilkent Univ., Ankara, Turkey, Jun. 2003.
24. P. Y. -Oijala and M. Taskinen, "Calculation of CFIE impedance matrix elements with RWG and n x RWG functions," IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 1837-1846, Aug. 2003.
25. R. D. Graglia, "On the numerical integration of the linear shape functions time 3-D gree's function or its gradient on a plane triangle," IEEE Trans. Antennas Propag., vol. 41, no 10, pp. 1448-1455, Oct. 1993.
26. W. C. Chew, J.-M. Jin E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Boston, MA: Artech House, 2001.
27. R. Coifman, V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propag. Mag., vol. 35, no. 3, pp. 7-12, Jun. 1993.
28. S. Koc, J. M. Song, and W. C. Chew, "Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem," SIAM J. Numer. Anal., vol. 36, no. 3, pp. 906-921, 1999.
29. Ö. Ergül and L. Gürel, "Enhancing the accuracy of the interpolations and anterpolations in MLFMA," IEEE Antennas Wireless Propag. Lett., vol. 5, pp. 467-470, 2006.
30. S. Velamparambil, W. C. Chew, and J. Song, "10 million unknowns: Is it that big?," IEEE Antennas Propag. Mag., vol. 45, no. 2, pp. 43-58, Apr. 2003.
31. Ö. Ergül and L. Gürel, "Optimal interpolation of translation operator in multilevel fast multipole algorithm," IEEE Trans. Antennas Propag., vol. 54, no. 12, pp. 3822-3826, Dec. 2006.
32. A. Brandt, "Multilevel computations of integral transforms and particle interactions with oscillatory kernels," Comp. Phys. Comm., vol. 65, pp. 24-38, Apr. 1991.
33. L. Gürel and W. C. Chew, "Recursive algorithms for calculating the scattering firom N strips or patches," IEEE Trans. Antennas Propag. vol. AP-38, pp. 507-515, Apr. 1990.
34. L. Gürel and Ö. Ergül, "Comparisons of FMM implementations employing different formulations and iterative solvers," in Proc. IEEE Antennas and Propag. Soc. Int. Symp., 2003, vol. 1, pp. 19-22.
35. L. Gürel and Ö. Ergül, "Fast and accurate solutions of integral-equation formulations discretised with tens of millions of unknowns," Electron. Lett., vol. 43, no. 9, pp. 499-500, Apr. 2007.
36. Ö. Ergül and L. Gürel, "Investigation of the inaccuracy of the MFIE discretized with the RWG basis functions," in Proc. IEEE Antennas and Propag. Soc. Int. Symp., 2004, vol. 3, pp. 3393-3396.
37. Ö. Ergül and L. Gürel, "Improved testing of the magnetic-field integral equation," IEEE Microw. Wireless Comp. Lett., vol. 15, no. 10, pp. 615-617, Oct. 2005.
38. Ö. Ergül and L. Gürel, "Solid-angle factor in the magnetic-field integral equation," Microw. Opt. Technol. Lett., vol. 45, no. 5, pp. 452-456, Jun. 2005.
39. Ö. Ergül and L. Gürel, "Improving the accuracy of the MFIE with the choice of basis functions," in Proc. IEEE Antennas and Propag. Soc. Int. Symp., 2004, vol. 3, pp. 3389-3392.
40. Ö. Ergül and L. Gürel, "On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems," presented at the Eur. Conf. Antennas and Propag. (EuCAP), 2006.
41. E. Ubeda 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," Microw. Opt. Technol. Lett., vol. 44, no. 4, pp. 354-358, Feb. 2005.
42. E. Ubeda and J. M. Rius, "Monopolar divergence-conforming and curl-conforming low-order basis functions for the electromagnetic scattering analysis," Microw. Opt. Technol. Lett., vol. 46, no. 3, pp. 237-241, Aug. 2005.
43. E. Ubeda and J. M. Rius, "Novel monopolar MFIE MoM-discretization for the scattering analysis of small objects," IEEE Trans. Antennas Propag., vol. 54, no. 1, pp. 50-57, Jan. 2006.
44. Ö. Ergül and L. Gürel, "The use of curl-conforming basis functions for the magnetic-field integral equation," IEEE Trans. Antennas Propag., vol. 54, no. 7, pp. 1917-1926, Jul. 2006.
45. L. C. Trintinalia and H. Ling, "First order triangular patch basis functions for electromagnetic scattering analysis," J. Electromagn. Waves and Appl., vol. 15, no. 11, pp. 1521-1537, 2001.
46. Ö. Ergül and L. Gürel, "Improving the accuracy of the magnetic field integral equation with the linear-linear basis functions," Radio Sci., vol. 41, Jul. 2006, RS4004, doi:10.1029/2005RS003307.
47. Ö. Ergül and L. Gürel, "Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations," IEEE Trans. Antennas Propag., vol. 55, no. 4, pp. 1103-1110, Apr. 2007.
48. C. P. Davis and K. F. Warnick, "High-order convergence with a low-order discretization of the 2-D MFIE," IEEE Antennas Wireless Propag. Lett., vol. 3, pp. 355-358, 2004.