Analysis of 3D microwave cavities using hierarchal vector finite elements

A set of hierarchal vector finite elements is used to predict the resonances of 3D microwave cavities. The elements are higher-order versions of an established curvilinear brick element. Like this element, they impose only tangential continuity on the field, and are therefore suitable for modelling abrupt material interfaces and sharp corners. They are also of mixed polynomial order to avoid spurious modes. Each element in the set is formed from lower elements by adding basis functions of higher polynomial order; the set is therefore hierarchal, and different element orders can be used side by side in the same mesh. The elements are applied to a number of resonance problems with known solutions: a cube, an empty cylindrical cavity, a length of ridge waveguide, a dielectric-loaded rectangular cavity and an enclosed microstrip patch