Generalized coupled azimuthal potentials for electromagnetic fields in inhomogeneous media

The original coupled azimuthal potential (CAP) formulation utilized two continuous potentials to represent the Fourier azimuthal modes of the vector field components in inhomogeneous axisymmetric material media. This formulation has since been used as the basis for finite-element solutions of radiation, scattering, and penetration problems. A generalization of the CAP formulation is presented that removes the restriction to axisymmetry of the inhomogeneous media while retaining the advantage of vector field generation in terms of only two scalar potentials. The discrete form of this generating relation is cast into a matrix transport equation, which is solved by the use of natural basis function. Variational and Galerkin approaches are considered for the solution of the given potentials. Computational examples, using finite elements, are given for the case of a simple three-dimensional boundary-value problem