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2022-01-30
Accurate and Efficient Evaluation of the Scattering of Bodies of Revolution Based on Magnetic Field Integral Equation
By
Progress In Electromagnetics Research M, Vol. 108, 1-15, 2022
Abstract
The integrals arising in magnetic field integral equation (MFIE) can become highly singular, rendering their numerical computation extremely challenging. Here, we propose a technique by which the singular integrals of the MFIE can be accurately and efficiently evaluated. In this technique, the corresponding integrals are separated into singular and regular parts. The regular parts are computed using a very simple Fast Fourier transform, whereas the remaining singular parts are evaluated based on two three-terms recurrence relations. The accuracy of the proposed method is demonstrated by analyzing the scattering of various bodies with smooth or non-smooth geometries and comparing the results with the literature.
Citation
Fahimeh Sepehripour, and Martijn Constant van Beurden, "Accurate and Efficient Evaluation of the Scattering of Bodies of Revolution Based on Magnetic Field Integral Equation," Progress In Electromagnetics Research M, Vol. 108, 1-15, 2022.
doi:10.2528/PIERM21112801
References

1. Ubeda, E., J. M. Rius, and A. Heldring, "Nonconforming discretization of the electric-field integral equation for closed perfectly conducting objects," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 8, 4171-4186, 2014.
doi:10.1109/TAP.2014.2325954        Google Scholar

2. Freno, B. A., W. A. Johnson, B. F. Zinser, D. R. Wilton, F. Vipiana, and S. Campione, "Characterization and integration of the singular test integrals in the method-of-moments implementation of the electric-field integral equation," Engineering Analysis with Boundary Elements, Vol. 124, No. 8, 185-193, 2021.
doi:10.1016/j.enganabound.2020.12.015        Google Scholar

3. Abdelmageed, A., "Efficient evaluation of modal Green's functions arising in EM scattering by bodies of revolution," Progress In Electromagnetics Research, Vol. 27, 337-356, 2000.
doi:10.2528/PIER99061601        Google Scholar

4. Mohsen, A. A. K. and A. K. Abdelmageed, "A fast algorithm for treating EM scattering by bodies of revolution," AEU - International Journal of Electronics and Communications, Vol. 55, No. 3, 164-170, 2001.
doi:10.1078/1434-8411-00025        Google Scholar

5. Yu, W. M., D. G. Fang, and T. J. Cui, "Closed form modal Green's functions for accelerated computation of bodies of revolution," IEEE Transactions on Antennas and Propagation, Vol. 56, No. 11, 3452-3461, 2008.
doi:10.1109/TAP.2008.2005459        Google Scholar

6. Hamed, S. M. A. and S. O. Bashir, "New exact series for modal Green's function," 2015 International Conference on Computing, Control, Networking, Electronics and Embedded Systems Engineering (ICCNEEE), 83-86, 2015.
doi:10.1109/ICCNEEE.2015.7381434        Google Scholar

7. Zubair, M., M. A. Francavilla, D. Zheng, F. Vipiana, and G. Vecchi, "Dual-surface electric field integral equation solution of large complex problems," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 6, 2577-2582, 2016.
doi:10.1109/TAP.2016.2552549        Google Scholar

8. Bolli, P., G. G. Gentili, R. Nesti, and G. Pelosi, "Coupled BORs scattering via an efficient MoM solution of CFIE," Microwave and Optical Technology Letters, Vol. 37, No. 3, 180-183, 2003.
doi:10.1002/mop.10861        Google Scholar

9. Yla-Oijala, P., "Numerical analysis of combined field integral equation formulations for electromagnetic scattering by dielectric and composite objects," Progress In Electromagnetics Research, Vol. 3, 19-43, 2008.
doi:10.2528/PIERC08032501        Google Scholar

10. 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, 1997.
doi:10.1002/(SICI)1098-2760(199701)14:1<9::AID-MOP4>3.0.CO;2-P        Google Scholar

11. Tong, M. S. and X. J. Huang, "Accurate solution of electromagnetic scattering by super-thin conducting objects based on magnetic field integral equation," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 10, 5633-5638, 2017.
doi:10.1109/TAP.2017.2734161        Google Scholar

12. Gurel, L. and O. Ergul, "Singularity of the magnetic-field integral equation and its extraction," IEEE Antennas and Wireless Propagation Letters, Vol. 4, No. 1, 229-232, 2005.
doi:10.1109/LAWP.2005.851103        Google Scholar

13. Ergul, O. and L. Gurel, "Improving the accuracy of the magnetic field integral equation with the linear-linear basis functions," Radio Science, Vol. 41, No. 4, 1-15, 2006.
doi:10.1029/2005RS003307        Google Scholar

14. Mohsen, A. A. K. and A. K. Abdelmageed, "Magnetic field integral equation for electromagnetic scattering by conducting bodies of revolution in layered media," Progress In Electromagnetics Research, Vol. 24, No. 3, 19-37, 1999.
doi:10.2528/PIER98122202        Google Scholar

15. Andreasen, M., "Scattering from bodies of revolution," IEEE Transactions on Antennas and Propagation, Vol. 13, No. 2, 303-310, 1965.
doi:10.1109/TAP.1965.1138406        Google Scholar

16. Mautz, J. R. and R. F. Harrington, "Radiation and scattering from bodies of revolution," Applied Scientific Research, Vol. 20, No. 1, 405-435, 1969.
doi:10.1007/BF00382412        Google Scholar

17. Glisson, A. W. and D. R. Wilton, "Simple and efficient numerical techniques for treating bodies of revolution,", Mississippi Univ University, 1979.        Google Scholar

18. Wood, W. D., A. W. Wood, and J. L. Fleming, "EM scattering from bodies of revolution using the locally corrected Nyström method," IEEE Antennas and Propagation Society Symposium, Vol. 4, 4036-4039, 2004.
doi:10.1109/APS.2004.1330236        Google Scholar

19. Vidal, C. F. V. P. and U. C. Resende, "Solution of integral equation in scattering analysis of conducting bodies of revolution by mom with first type elliptic integrals," Proceedings of the IV International Conference on Computational Methods for Coupled Problems, 1232-1238, 2011.        Google Scholar

20. Lai, J. and M. O'Neil, "A fast and high order algorithm for the electromagnetic scattering of axis-symmetric objects," 2018 IEEE International Conference on Computational Electromagnetics (ICCEM), 1-2, 2018.        Google Scholar

21. Gedney, S. and R. Mittra, "The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution," IEEE Transactions on Antennas and Propagation, 92-95, 1988.        Google Scholar

22. Gedney, S. D. and R. Mittra, "The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution," IEEE Transactions on Antennas and Propagation, Vol. 38, No. 3, 313-322, 1990.
doi:10.1109/8.52253        Google Scholar

23. Tong, M. S. and W. C. Chew, "Evaluation of singular Fourier coefficients in solving electromagnetic scattering by body of revolution," Radio Science, Vol. 43, No. 4, 1-9, 2008.
doi:10.1029/2007RS003755        Google Scholar

24. Su, T., D. Ding, Z. Fan, and R. Chen, "Efficient analysis of EM scattering from bodies of revolution via the ACA," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 2, 983-985, 2013.
doi:10.1109/TAP.2013.2292079        Google Scholar

25. Gibson, W. C., The Method of Moments in Electromagnetics, CRC Press, 2014.
doi:10.1201/b17119

26. Schmitz, J. L., "Efficient solution for electromagnetic scattering using the dual-surface magnetic-field integral equation for bodies of revolution," Proceedings of IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting, 2318-2321, 1994.
doi:10.1109/APS.1994.408019        Google Scholar

27. Fleming, J. L., A. W. Wood, and J. W. D. Wood, "Locally corrected Nyström method for EM scattering by bodies of revolution," Journal of Computational Physics, Vol. 196, No. 1, 41-52, 2004.
doi:10.1016/j.jcp.2003.10.029        Google Scholar

28. Ubeda Farré, E., Contribution to the Improvement of Integral Equation Methods for Penetrable Scatterers, Universitat Politècnica de Catalunya, 2001.

29. Resende, U. C., F. J. S. Moreira, and O. M. C. Pereira-Filho, "Efficient evaluation of singular integral equations in moment method analysis of bodies of revolution," Journal of Microwaves, Optoelectronics and Electromagnetic Applications (JMOe), Vol. 6, No. 2, 373-391, 2007.        Google Scholar

30. Vaessen, J. A. H. M., M. C. van Beurden, and A. G. Tijhuis, "Accurate and efficient computation of the modal Green's function arising in the electric-field integral equation for a body of revolution," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 7, 3294-3304, 2012.
doi:10.1109/TAP.2012.2196911        Google Scholar

31. Trefethen, L. N. and J. Weideman, "The exponentially convergent trapezoidal rule," SIAM Review, Vol. 56, No. 3, 385-458, 2014.
doi:10.1137/130932132        Google Scholar

32. Biggs, F., L. B. Mendelsohn, and J. B. Mann, "Hartree-Fock Compton profiles for the elements," Atomic Data and Nuclear Data Tables, Vol. 16, No. 3, 201-309, 1975.
doi:10.1016/0092-640X(75)90030-3        Google Scholar

33. Wolfram Research, NIntegrate, Wolfram Language function, https://reference.wolfram.com/language/ref/NIntegrate.html, 1988 (updated 2014).        Google Scholar

34. Umashankar, K. R., "Numerical analysis of electromagnetic wave scattering and interaction based on frequency-domain integral equation and method of moments techniques," Wave Motion, Vol. 10, No. 6, 493-525, 1988.
doi:10.1016/0165-2125(88)90010-8        Google Scholar

35. Harrington, R. F., "The method of moments in electromagnetics," Journal of Electromagnetic Waves and Applications, Vol. 1, No. 3, 181-200, 1987.
doi:10.1163/156939387X00018        Google Scholar

36. Vaessen, J. A. H. M., Efficient Modeling of Electromagnetic Fields in Stochastic Configurations, Technische Universiteit Eindhoven, 2015.