The use of hierarchical triangles an finite-element analysis of microwave and optical devices

Hierarchical triangles are high-order finite elements, which permit mixing of orders within the same mesh. They are particularly useful in microwave and optical problems, where the underlying wave-like variation of the field is modeled better by high-order than low-order elements, but where the use of the same order throughout gives an inefficient distribution of degrees of freedom. Fields computed with hierarchical elements are shown for a microstrip patch, two posts in a rectangular waveguide, and a dielectric waveguide feed.