Finite element solution of longitudinally magnetized elliptical gyromagnetic waveguides

The classic method used to derive a functional is to construct a quadratic form by premultiplying the wave equation by the conjugate field and then integrating this quantity over the cross section of the problem region. This procedure is utilized to construct a solution of the longitudinally magnetized gyromagnetic problem using the z-directed coupled wave equations. It is used in conjunction with the finite-element method to evaluate the propagation constants of an elliptical gyromagnetic waveguide with either an electric or a magnetic wall. The well-known functionals associated with the four possible planar circuits made up of electric and magnetic side, and top and bottom walls, are obtained directly from those of the related waveguide problems