Implementation of arbitrarily high order hierarchical vector basis functions for the finite element analysis of a rectangular waveguide

In any computational field there is an ever-present drive for better computational efficiency. This also holds true in the field of computational electro-magnetics where the finite element method (FEM) is regularly used. To improve the efficiency of a solution, various higher order basis functions are often employed. Two closely related sets of basis functions are considered, namely those implemented by Webb [1] and those of Slone [2] which are given as a correction to Webb's original basis functions. To facilitate the comparison between these two sets of basis functions, an efficient representation scheme is devised which allows for generation of these basis functions to any order. This representation is then used to perform a direct comparison between the results for the eigen-analysis of a rectangular PEC waveguide in two dimensions.