Decreasing the dimension of a system of scalar equations in the solution of diffraction problems

Abstract

A vector integral equation is constructed, and an algebraic representation of the equation is considered in the solution of a boundary-value problem in an ideally conducting polyhedron. Moreover, due to the introduction of local coordinate systems on each of the faces of the ideally conducting polyhedron, the integral vector equation relative to the three constituents of the surface current reduces to a system of two scalar integral equations relative to the corresponding components of the current, expressed in the local coordinate systems.