Boundary Conditions

Electromagnetic scattering from complex objects has been an area of in-depth research for many years. A variety of solution methodologies have been developed and utilised for the solution of ever increasingly complex problems. Among these methodologies, the subject of impedance boundary conditions has interested the authors for some time. In short, impedance boundary conditions allow one to replace a complex structure with an appropriate impedance relationship between the electric and magnetic fields on the surface of the object. This simplifies the solution of the problem considerably, allowing one to ignore the complexity of the internal structure beneath the surface. This book examines impedance boundary conditions in electromagnetics. The introductory chapter provides a presentation of the role of the impedance boundary conditions in solving practical electromagnetic problems and some historical background. One of the main objectives of this book is to present a unified and thorough discussion of this important subject. A method based on a spectral domain approach is presented to derive the Higher Order Impedance Boundary Conditions (HOIBC). The method includes all of the existing approximate boundary conditions, such as the Standard Impedence Boundary Condition, the Tensor Impedence Boundary Condition and the Generalised Impedance Boundary Conditions, as special cases. The special domain approach is applicable to complex coatings and surface treatments as well as simple dielectric coatings. The spectral domain approach is employed to determine the appropriate boundary conditions for planar dielectric coatings, chiral coatings and corregated conductors. The accuracy of the proposal boundary conditions is discussed. The approach is then extended to include the effects of curvature and is applied to curved dielectric and chiral coatings. Numerical data is presented to critically assess the accuracy of the results obtained using various forms of the impedence boundary conditions. A number of appendices that provide more detail on some of the topics addressed in the main body of the book and a selective list of references directly related to the topics addressed in this book are also included.