TABLE OF CONTENTS A first order boundary condition contains a single scalar or tensor impedance ? which can be used to simulate the scattering properties of the surface. It represents a refinement of the conditions for ideal (pec or pmc) surfaces, and includes these as special cases, but the accuracy produced is not always sufficient. One way to improve the accuracy is to include additional derivatives of the field to create a higher order boundary condition with more degrees of freedom. The order is specified by the highest derivative present in one manifestation of the condition.
The earliest example is the second order condition developed by Rytov (1940) to model the planar surface of a highly conducting material, but there is no evidence that the condition was ever used other than to help establish the validity of the first order one. A quarter of a century later Karp and Karal (1965) proposed a class of generalised impedance boundary conditions (now abbreviated to GIBCs) which they used to model a metal-backed dielectric layer whose thickness was sufficient to support more than one surface wave. They showed how to determine the coefficients and how the accuracy is affected by the layer thickness and the order of the condition but, prior to this, higher order conditions had come into use in mechanics.
For a hydroacoustic wave incident on a thin elastic plate, the assumption of an infinitesimally thin plate leads to a boundary (or transition) condition which is actually a fifth order one...
