Numerical calculation of the diffraction coefficients for an arbitrary shaped perfectly conducting cone

A method for numerical calculation of the diffraction coefficients for electromagnetic diffraction by arbitrarily shaped perfectly conducting cones is proposed. The approach makes an extensive use of the analytic formulas of Smyshlyaev in combination with further developments, including a use of the potential theory adapted to the Laplace-Beltrami operator on a subdomain of unit sphere. This reduces the problem to a Fredholm integral equation on the closed curve of the unit sphere (defining the cone's geometry) which can be solved numerically. This strategy permits us to implement a numerical code for calculation of the diffraction coefficients for cones of rather general cross sections. Results of sample calculations for the circular and elliptic cones are given.