Stable coaxial waveguide-port algorithm for the time-domain finite-element method

A new coaxial waveguide-port algorithm is developed and tested for the time-domain finite-element method. The electric field is modeled by edge elements and, for part of a coaxial cable or a similar transmission line, the full Maxwell's equations are reduced to the one-dimensional transmission-line equation through the use of macro elements, which represent the dominant waveguide mode. The port algorithm converges quadratically with the cell size for geometries with smooth boundaries, which is demonstrated by tests on a coaxial cable with a short-circuit termination. The pan algorithm is proven to be stable up to the Courant limit of the explicit scheme used for the transmission-line equation, without any added artificial dissipation. The proposed port algorithm preserves, by construction, the reciprocity of Maxwell's equations. For a 2 × 2-array of patch antennas, computation of the coupling of the antenna elements demonstrates that the scattering matrix is symmetric or, equivalently, that the proposed algorithm preserves reciprocity.