In this final chapter, we discuss a selection of more advanced topics, primarily relating to the finite element method. However, as will be seen, a linkage to the method of moments will be established, and perhaps rather less expectedly, the finite difference time domain method will also emerge as a special case of a finite element time domain treatment, so amongst other purposes, the chapter serves to draw together these three apparently quite different methods.

We will start by considering a very important extension of the vector elements, namely higher-order elements. Following this, the stationary functional formulation for deterministic (driven) problems will be outlined. In the preceding chapter, an eigenvalue problem was used to illustrate the FEM in two dimensions; in this chapter, a deterministic three-dimensional problem will be discussed, namely the analysis of waveguide obstacles. Finite element analysis is ideal for this problem, and good results have been obtained by a number of workers. Results for two waveguide problems computed using FEM codes incorporating higher-order elements will be shown. Then, a hybrid FEM/MoM formulation, which has proven very powerful for specialized applications, will be introduced, and an application to radiation exposure assessment near a base-station antenna will be presented. Following this, time domain finite element analysis is briefly discussed.

We conclude the chapter with a discussion on two issues which impact on efficiency. Firstly, sparse matrix storage schemes are briefly outlined, and secondly, error estimation and the use of mesh adaptation based on this is discussed.