Covariant-projection quadrilateral elements for the analysis of waveguides with sharp edges

Covariant-projection elements are shown to be a good way of finding the dispersion characteristics of arbitrarily shaped waveguides. They have been demonstrated to produce no spurious modes, and because only tangential continuity is imposed between elements, either the electric field or the magnetic field may be calculated in the presence of dielectric and magnetic materials. Waveguides with sharp metal edges may be analyzed more efficiently than with other methods. Results are presented for a rectangular waveguide half loaded with dielectric, a double-ridged waveguide, a shielded microstrip line, and coupled microstrip lines on a cylindrical substrate. The matrices generated are sparse. and the number of zero eigenvalues produced is predictable. It therefore seems likely that the algebraic problem can be solved by sparse techniques, which would make the method applicable to even more complicated geometries at a modest computational cost