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Computation of Physical Optics Integral by Levin's Integration Algorithm

By Ahmet Cemal Durgun and Mustafa Kuzuoğlu
Progress In Electromagnetics Research M, Vol. 6, 59-74, 2009


In this paper, a novel algorithm for computing Physical Optics (PO) integrals is introduced. In this method, the integration problem is converted to an inverse problem by Levin's integration algorithm. Furthermore, the singularities, that are possible to occur in the applications of Levin's method, are handled by employing trapezoidal rule together with Levin's method. Finally, the computational accuracy of this new method is checked for some radar cross section (RCS) estimation problems performed on flat, singly-curved and doubly-curved PEC plates which are modeled by 8-noded isoparametric quadrilaterals. The results are compared with those obtained by analytical and brute force integration.


Ahmet Cemal Durgun and Mustafa Kuzuoğlu, "Computation of Physical Optics Integral by Levin's Integration Algorithm," Progress In Electromagnetics Research M, Vol. 6, 59-74, 2009.


    1. Ludwig, A. C., "Computation of radiation patterns involving double integration," IEEE Transactions on Antennas and Propagation, Vol. 16, No. 6, 767-769, November 1968.

    2. Dos Santos, M. L. X. and N. R. Rabelo, "On the Ludwig integration algorithm for triangular subregions," Proceedings of the IEEE, Vol. 74, No. 10, 1455-1456, October 1986.

    3. Moreira, F. J. S. and A. Prata, "A self-checking predictor-corrector algorithm for efficient evaluation of reflector antenna radiation integrals," IEEE Transactions on Antennas and Propagation, Vol. 42, No. 2, 246-254, January 1994.

    4. Kobayashi, H., K. Hongo, and I. Tanaka, "Expressions of physical optics integral for smooth conducting scatterers approximated by quadratic surfaces ," Electronics and Communication in Japan, Vol. 83, No. 7, 863-871, Part 1, 2000.

    5. Flinn, E. A., "A modification of Filon's method of numerical integration," Journal of the ACM, Vol. 7, No. 2, 181-184, April 1960.

    6. Crabtree, G. D., "A numerical quadrature technique for physical optics scattering analysis," IEEE Transactions on Magnetics, Vol. 27, No. 5, 4291-4294, September 1991.

    7. Vico, F., M. Ferrando, M. Baquero, and E. Antonino, "A new 3D fast physical optics method," IEEE Antennas and Propagation Society International Symposium 2006, 1849-1852, July 9-14, 2006.

    8. Corona, P., G. Manara, G. Pelosi, and G. Toso, "PO analysis of the scattering from polygonal flat-plate structures with dielectric inclusions," Journal of Electromagnetic Waves and Applications, Vol. 14, 693-711, 2000.

    9. Arslanagic, S., P. Meincke, E. Jorgensen, and O. Breinbjerg, "An exact line integral representation of the physical optics far field from plane PEC scatterers illuminated by Hertzian dipoles," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 1, 51-69, 2003.

    10. Levin, D., "Procedures for computing one and two dimensional integrals of fumctions with rapid irregular oscillations," Mathematics of Computation, 531-538, April 1982.

    11. Kuzuoglu, M., "Solution of electromagnetic boundary value problems by the plane wave enriched FEM approach," IEEE APS-URSI International Symposium, 2003.

    12. Taylor, C. and T. G. Hughes, Finite Element Programming of the Navier-Stokes Equations, Pineridge Press, 1981.