Implementation and performance comparison for higher order triangular vector elements

Based on H₁(curl) triangular interpolatory vector elements, explicit forms of the elemental matrices for the higher order vector elements are presented completely by using the classified bases and block matrix technique, the explicit results of integration matrices are also given. The results of a numerical experiment that investigates the eigen-problem of a rectangular waveguide, compare the performance of different vector elements systematically (such as calculated accuracy, condition numbers, selectivity of the facet related basis functions), which are also applied to the eigen-solution of homogeneously-filled waveguides. The methods can be extended to the analysis of 3D, ultra higher order, hierarchical vector elements with any type effectively.