Recently, a new analytically regularizing procedure, based on Helmholtz decomposition and Galerkin method, has been proposed to analyze the electromagnetic scattering from a zero-thickness perfectly electrically conducting disk. The convergence of the discretization scheme is guaranteed and of exponential type, i.e., few expansion functions are needed to achieve highly accurate solutions. However, it leads to the numerical evaluation of improper integrals of asymptotically oscillating and slowly decaying functions. Asymptotic acceleration techniques allow to obtain faster decaying integrands without overcoming the problem of the oscillating nature of the integrands themselves, i.e., the convergence of the integrals becomes slower and slower as the accuracy required for the solution is higher. In this paper, by means of algebraic manipulations and a suitable integration procedure in the complex plane, an alternative expression for the scattering matrix coefficients involving only fast converging proper integrals is devised. As shown in the numerical results section, the proposed technique is very effective and drastically outperforms the classical analytical asymptotic acceleration technique.
2. Nosich, A. I., "Method of analytical regularization in computational photonics," Radio Science, Vol. 8, 1421-1430, 2016.
3. Hongo, K. and H. Serizawa, "Diffraction of electromagnetic plane wave by rectangular plate and rectangular hole in the conducting plate," IEEE Trans. Antennas Propag., Vol. 47, No. 6, 1029-1041, 1999.
4. Bliznyuk, N. Y., A. I. Nosich, and A. N. Khizhnyak, "Accurate computation of a circular-disk printed antenna axisymmetrically excited by an electric dipole," Microwave and Optical Technology Letters, Vol. 25, No. 3, 211-216, 2000.
5. Tsalamengas, J. L., "Rapidly converging direct singular integral-equation techniques in the analysis of open microstrip lines on layered substrates," IEEE Trans. Microw. Theory Tech., Vol. 49, No. 3, 555-559, 2001.
6. Losada, V., R. R. Boix, and F. Medina, "Fast and accurate algorithm for the short-pulse electromagnetic scattering from conducting circular plates buried inside a lossy dispersive half-space," IEEE Trans. Geosci. Remote Sensing, Vol. 41, 988-997, 2003.
7. Lucido, M., G. Panariello, and F. Schettino, "Accurate and efficient analysis of stripline structures," Microwave and Optical Technology Letters, Vol. 43, 14-21, 2004.
8. Hongo, K. and Q. A. Naqvi, "Diffraction of electromagnetic wave by disk and circular hole in a perfectly conducting plane," Progress In Electromagnetics Research, Vol. 68, 113-150, 2007.
9. Coluccini, G., M. Lucido, and G. Panariello, "TM scattering by perfectly conducting polygonal cross-section cylinders: A new surface current density expansion retaining up to the second-order edge behavior," IEEE Trans. Antennas Propag., Vol. 60, No. 1, 407-412, 2012.
10. Lucido, M., "An analytical technique to fast evaluate mutual coupling integrals in spectral domain analysis of multilayered coplanar coupled striplines," Microwave and Optical Technology Letters, Vol. 54, No. 4, 1035-1039, 2012.
11. Coluccini, G., M. Lucido, and G. Panariello, "Spectral domain analysis of open single and coupled microstrip lines with polygonal cross-section in bound and leaky regimes," IEEE Trans. Microw. Theory Tech., Vol. 61, No. 2, 736-745, 2013.
12. Lucido, M., "An efficient evaluation of the self-contribution integrals in the spectral-domain analysis of multilayered striplines," IEEE Antennas and Wireless Propagation Letters, Vol. 12, 360-363, 2013.
13. Coluccini, G. and M. Lucido, "A new high efficient analysis of the scattering by a perfectly conducting rectangular plate," IEEE Trans. Antennas Propag., Vol. 61, No. 5, 2615-2622, 2013.
14. Lucido, M., G. Panariello, and F. Schettino, "An EFIE formulation for the analysis of leaky-wave antennas based on polygonal cross-section open waveguides," IEEE Antennas and Wireless Propagation Letters, Vol. 13, 983-986, 2014.
15. Di Murro, F., M. Lucido, G. Panariello, and F. Schettino, "Guaranteed-convergence method of analysis of the scattering by an arbitrarily oriented zero-thickness PEC disk buried in a lossy half-space," IEEE Trans. Antennas Propag., Vol. 63, No. 8, 3610-3620, 2015.
16. Lucido, M., F. Di Murro, G. Panariello, and C. Santomassimo, "Fast converging CFIE-MoM analysis of electromagnetic scattering from PEC polygonal cross-section closed cylinders," Progress In Electromagnetics Research B, Vol. 74, 109-121, 2017.
17. Kantorovich, L. V. and G. P. Akilov, Functional Analysis, 2nd Ed., Pergamon Press, Oxford-Elmsford, N.Y., 1982.
18. Lucido, M., G. Panariello, and F. Schettino, "Scattering by a zero-thickness PEC disk: A new analytically regularizing procedure based on Helmholtz decomposition and Galerkin method," Radio Science, Vol. 52, No. 1, 2-14, 2017.
19. Park, S. and C. A. Balanis, "Dispersion characteristics of open microstrip lines using closed-form asymptotic extraction," IEEE Trans. Microw. Theory Tech., Vol. 45, No. 3, 458-460, Mar. 1997.
20. Park, S. and C. A. Balanis, "Closed-form asymptotic extraction method for coupled microstrip lines," IEEE Microw. Guided Wave Lett., Vol. 7, No. 3, 84-86, Mar. 1997.
21. Amari, S., R. Vahldieck, and J. Bornemann, "Using selective asymptotics to accelerate dispersion analysis of microstrip lines," IEEE Trans. Microw. Theory Tech., Vol. 46, No. 7, 1024-1027, Jul. 1998.
22. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Verlag Harri Deutsch, The Netherlands, 1984.
23. Geng, N. and L. Carin, "Wide-band electromagnetic scattering from a dielectric BOR buried in a layered lossy dispersive medium," IEEE Trans. Antennas Propag., Vol. 47, 610-619, 1999.