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A Low-Order-Singularity Electric-Field Integral Equation Solvable with Pulse Basis Functions and Point Matching

By Robert Shore and Arthur Yaghjian
Progress In Electromagnetics Research, Vol. 52, 129-151, 2005


The conventional form of the electric-field integral equation (EFIE), unlike the magnetic-field integral equation, cannot be solved accurately with the method of moments using pulse basis functions and point matching. A new form of the EFIE is derived whose kernel has no greater singularity than that of the free-space Green's function. This low-order-singularity form of the EFIE, the LEFIE, is solved numerically for perfectly electrically conducting bodies of revolution (BORs) using pulse basis functions and point-matching. Derivatives of the current are approximated with finite differences using a quadratic Lagrangian interpolation polynomial. Such a simple solution of the LEFIE is contingent, however, upon the vanishing of a linear integral that appears when the original EFIE is transformed to obtain the LEFIE. This generally restricts the applicability of the LEFIE to smooth closed scatterers. Bistatic scattering calculations performed for a prolate spheroid demonstrate that results comparable in accuracy to those of the conventionally solved EFIE can be obtained with the LEFIE using pulse basis functions and point matching provided a higher density of points is used close to the ends of the BOR.


 (See works that cites this article)
Robert Shore and Arthur Yaghjian, "A Low-Order-Singularity Electric-Field Integral Equation Solvable with Pulse Basis Functions and Point Matching," Progress In Electromagnetics Research, Vol. 52, 129-151, 2005.


    1. Maue, A. W., "On the formulation of a general scattering problem by means of an integral equation," Z. Phys., Vol. 126, 601-618, 1949.

    2. Van Bladel, J., Electromagnetic Fields, McGraw-Hill, New York, 1964.

    3. Yaghjian, A. D., "Augmented electric-and magnetic-field integral equations," Radio Science, Vol. 16, No. 12, 987-1001, 1981.

    4. Mautz, J. R. and R. F. Harrington, "H-field, E-field, and combined-field solutions for conducting bodies of revolution," Arch. Math. Ubertragungtech., Vol. 32, 157-164, 1978.

    5. Yaghjian, A. D. and M. B. Woodworth, "Derivation, application and conjugate gradient solution of the dual-surface integral equations for three-dimensional, multiwavelength perfect conductors," Progress in Electromagnetics Research, Vol. 5, 103-130, 1991.

    6. Woodworth, M. B. and A. D. Yaghjian, "Multiwavelength three-dimensional scattering with dual-surface integral equations," J. Opt. Soc. Am. A, Vol. 11, No. 4, 1399-1413, 1994.

    7. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, New York, 1998.

    8. Shore, R. A. and A. D. Yaghjian, Dual surface electric field equation, Air Force Research Laboratory Report, AFRL-SN-HS-TR-2001-013, 2001.

    9. Shore, R. A. and A. D. Yaghjian, "Dual-surface integral equations in electromagnetic scattering," Proceedings International Union of Radio Science (URSI) 27th General Assembly, No. 8, 2002.

    10. Pearson, C. E., Numerical Methods in Engineering and Science, Van Nostrand Reinhold, New York, 1986.

    11. Shore, R. A. and A. D. Yaghjian, "A low-order-singularity electric-field integral equation solvable with pulse basis functions and point matching," AFRL Technical Report.

    12. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley, New York, 1989.

    13. Yaghjian, A. D., "Near field antenna measurements on a cylindrical surface: A source scattering matrix formulation," NBS Technical Note, No. 696, 1977.

    14. Putnam, J. M. and L. N. Medgyesi-Mitschang, "Combined field integral equation formulation for axially inhomogeneous bodies of revolution," McDonnell Douglas Research Laboratories MDC Report, No. QA003, 1987.