Boundary integral equation technique defined on a spherical surface with different applications in electromagnetics and acoustics

A boundary integral equation technique is presented which is defined on a spherical surface. This technique can be used in electromagnetics to determine the singular behaviour of the fields at the common tip of a number of bi-isotropic cones with arbitrary cross-section. The technique is also applicable for electromagnetic conical waveguides and acoustical horns with hard walls with arbitrary cross-section. The Green´s function in the integral equation is an associated Legendre function. The integral equation is solved with the method of moments combined with the method of Galerkin.