The helix antenna discussed in the previous chapter used a new type of element to model surfaces. The theory underlying this is described in this chapter. Not only is the basic theory quite complex, but implementations are especially challenging, so we focus largely on an introductory discussion, followed by some examples of using available codes, rather than going into the frequently lengthy details of full 3D implementations. We will see that not only can perfectly (or highly) conducting structures be efficiently modelled using surface currents, but also homogeneous dielectric and/or magnetic regions, using fictitious equivalent currents. (We will even briefly describe how inhomogeneous bodies can be modelled using volumetric currents, but note at the outset that this is not one of the strong points of the MoM.) Modelling surfaces is far more computationally expensive than modelling wires, and some methods for reducing the computational cost will also be discussed. These include a hybrid of the MoM and physical optics, and the general class of fast methods, including both those based on the FFT and the fast multipole method. We will also briefly touch on the use of parallel processing.

Electric and magnetic field integral equations

Following the same lines as the Pocklington equation (Chapter 4), integral equations in either the magnetic or electric fields can be derived for problems with currents flowing on surfaces. The derivation is quite complex, and only the results will be presented here.