Singularities of green's function in surface integral equations

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Abstract
A method based on the integral equation defined on the boundary of an object often is used to analyze numerically scattering or antenna problems. However, depending on the boundary condition or body shape, a surface integral is required which includes the second‐order derivative of Green's function. In general, this integral diverges due to the singularity of Green's function. However, its finite portion converges. When the finite portion of a diverging integral is evaluated numerically, processing of the singularity cannot be treated accurately in numerical calculation. A method is presented here in which the finite portion of the diverging integral is evaluated analytically in a finite region and only the nondiverging portion is evaluated numerically. A formulation is presented in which the singularity of the second derivative of Green's function is removed. the present method is applied to examples of two‐dimensional problems. As an example of three‐dimensional problems, the method is applied to a cylindrical antenna. In the latter case, the equation for the electric field becomes extremely simple and Galerkin's method can be applied if piecewise sinusoidal functions are used as the expansion functions. It is shown by means of numerical examples that extremely thin as well as thick antennas can be analyzed.

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