Approximate boundary conditions provide an approximate relationship between the electric and magnetic field on a chosen surface. In general, their purpose is to simplify the analytical or numerical solution of wave problems involving complex structures. They are important in all disciplines, e.g. acoustics, hydrodynamics and electromagnetics, where boundary conditions are involved, and are becoming more so as we seek to model more complicated situations. Some versions have also been around for a long time and, although the classical condition E _tan = 0 at the surface of a metal is often regarded as exact, it is in fact an approximation for all metals even at microwave frequencies.

In electromagnetics (to which we shall devote our attention) approximate boundary conditions are now widely used in scattering, propagation and waveguide analyses to simulate the material and geometric properties of surfaces. Take, for example, a finite body immersed in a homogeneous medium and illuminated by an electromagnetic field. Knowing the material properties of the body, it is possible, in principle, to find the scattered field exterior to the body, by taking into account the behaviour of the fields within the body. However, the task would be greatly simplified if the properties could be simulated via a boundary condition involving only the external fields imposed at the outer surface, thereby converting a two (or more) media problem into a single medium one. This is the objective of an approximate boundary condition. Although it is generally convenient for the surface of the actual body...