New trends in hierarchical vector basis functions

This chapter reviews recent advances in computational electromagnetics regarding simple techniques for the systematic construction of higher order vector bases used by advanced numerical codes. Higher order functions are used in numerical solutions of differential and integrodifferential equations by the application of the finite element method (FEM) and the method of moments (MoM). First, we consider divergence-conforming and curl-conforming polynomial vector bases and then introduce substitutive and additive vector bases that are able to model field singularities in the vicinity of edges or vertices. The advantages offered by the use of these higher order models are illustrated by numerical results. Mathematical aspects and numerical techniques presented in this chapter are dealt with in detail in [1], except for the most recent developments concerning singular vector basis functions and their numerical implementation. For background information and further details, the interested reader may refer to [1] and references therein.