Integral equation numerical approach for the determination of the diffraction coefficients from generally shaped cones

Purpose This paper aims to numerically solve the integral equations that arise during the process of determining the cone diffraction coefficients and to validate the solutions using different analytical and numerical methods. Design/methodology/approach A formulated method of moments (MoM) solution for the Green’s function, defined by the Laplace-Beltrami operator on the surface of the unit sphere, is attempted. The boundary is assumed to have an arbitrary shape and is approximated by dividing it into a set of points connected by curvilinear segments. The boundary conditions – whether Dirichlet or Neumann – result in two distinct integral equations, each requiring separate treatment. To reduce computational time and complexity, unit pulses are used as the basis and test functions. Finite Differences are also constructed for completeness and validation of the formulated MoM solution. Findings MoM appears more suitable compared to other numerical methods for finding the diffraction coefficients from generally shaped cones. Originality/value The originality of this paper lies in the application of the MoM in such a way that it can be applied to cones with an arbitrary cross section (defined the intersection between the cone surface and the unit sphere), as well as the choice of the basis and test functions and the edge-refined technique that reduces the computational time of the algorithm.