This book covers the latest problems of modern mathematical methods for three-dimensional problems of diffraction by arbitrary conducting screens. This comprehensive study provides an introduction to methods of constructing generalized solutions, elements of potential theory, and other underlying mathematical tools. The problem settings, which turn out to be extremely effective, differ significantly from the known approaches and are based on the original concept of vector spaces 'produced' by Maxwell equations. The formalism of pseudodifferential operators enables to prove uniqueness theorems and the Fredholm property for all problems studied. Readers will gain essential insight into the state-of-the-art technique of investigating three-dimensional problems for closed and unclosed screens based on systems of pseudodifferential equations. A detailed treatment of the properties of their kernels, in particular degenerated, is included. Special attention is given to the study of smoothness of generalized solutions and properties of traces.

This book describes new, highly effective, rigorous analysis methods for electromagnetic wave problems. Examples of their application to the mathematical modelling of micros trip lines, corrugated flexible waveguides, horn antennas, complex-shaped cavity resonators and periodic structures are considered. Special attention is paid to energy dissipation effects. Various physical models and methods of analysis of dissipation are described and approximate formulas and computer-based calculation results for dissipation characteristics are given and compared with experimental data. Ways of decreasing dissipation in waveguides and resonators are discussed. The book will be of interest to physicists and engineers working on the theory and design of microwave and millimetre-wave components and devices. Designers in microwave engineering will find here all the information they need for choosing the correct waveguide (resonator) for a stipulated dissipation characteristic. The numerical algorithms and formulas can be directly applied to CAD systems. The book is also relevant for students of electromagnetism and microwave circuits.