The initial boundary value problems considered in the book describe the transient electromagnetic fields formed by open periodic, compact, and waveguide resonators. The methods and algorithms which are developed and the mathematical and physical results obtained provides a basis on which a modern theory for the scattering of resonant non-harmonic waves can be developed. The need for the creation of such a theory is acutely felt in the many applications of resonant pulsed fields, since accurate and reliable modeling of their formation, radiation, and scattering are to a large extent lacking. One of the principal goals of the book is to present solidly based and robust algorithms for such structures with substantially increased efficiency that allow the extraction of complete and accurate information concerning the scattering of transient electromagnetic waves by complex objects. The determination and visualization of the electromagnetic fields in such situations, based on realistic models for the material parameters and geometrical shape, simplifies and significantly speeds up the solution of a wide class of fundamental and applied problems in electromagnetic field theory.

The book provides a systematic approach to scattering of transient fields which, with advantage, can be introduced in undergraduate or graduate courses in theoretical and applied radiophysics and different engineering specialities, such as antenna and wave-guide technology. More generally, the book should be of interest to scientists in applied mathematics, computer science and computational physics.