Integral Equations and Iteration Methods in Electromagnetic Scattering

The analysis of scattering of electromagnetic waves in inhomogeneous three-dimensional bounded media is extremely important from both theoretical and practical viewpoints, and constitutes the core family of problems in electromagnetics.

In this monograph the following fundamental topics relating to these problems are considered: mathematical problems and methods related to the scattering of electromagnetic waves by inhomogeneous three-dimensional anisotropic bodies and their reduction to volume singular integral equations; iteration techniques for solving linear operator equations; and efficient methods for solving volume integral equations that employ iteration procedures. Nowadays, volume singular integral equations are widely used as an efficient tool of numerical solution to the problems of complicated three-dimensional structures.

Analysis of integral equations and corresponding scattering problems, including nonclassical ones, is performed in the general formulation. The necessary and sufficient conditions that provide fulfilment of the Noether property of operators and sufficient conditions for the Fredholm property are obtained. Existence and uniqueness theorems for scattering problems considered in both classical and nonclassical settings are proved. Much attention is given to iteration techniques and development of corresponding computational algorithms.

This monograph will be of interest to researchers in electromagnetics, integral equations, iteration methods and numerical analysis both in academia and industry.