The up-to-date methodology of data accessing that is based on mathematical simulation and computational experiment is realized in electromagnetics through the solution of boundary-value (frequency domain) and initial boundary-value (time domain) problems for Maxwell’s equations. In the recent years, research in the pulsed wave radiation, propagation, and scattering has been carried out very intensively. The reason is that design of a whole number of communication, electronic, and radar devices has required a reliable data on spatial-temporal and spatial-frequency field transformations in rather complex electrodynamic structures, whereas the potentialities of standard frequency-domain approaches in this respect either substantially limited or have already been exhausted. Amongst other attractive features of the time-domain approaches are the following:

• they are free from the idealizations inherent in the frequency domain;

• they are universal owing to minimal restrictions imposed on geometrical and material parameters of the objects under study;

• they allow explicit computational schemes, which do not require inversion of any operators and call for an adequate run time when implementing on present-day computers;

• they result in data easy convertible into a standard set of frequency-domain characteristics.

At the same time, a number of problems in the theory of transient electromagnetic fields have not yet found their universal, valid, and practically feasible solutions. This fact unfavorably affects a quality of model constructions and restricts the potentialities of the time-domain methods in the study of transient processes and spatial-temporal transformations of pulsed waves. Among the problems of this kind, mention may be made of the problem of correct and efficient truncation of the computational domain in the so called open problems, i.e. in the problems whose analysis domains are infinite along one or more spatial coordinates. In addition, we may point out the problem of far-field zone, the problem of large and remote field sources, and others.

The book is concerned with mathematical simulation and physical analysis of transient and steady-state processes in open resonant electrodynamic structures that generate, guide, scatter, and radiate pulsed and monochromatic electromagnetic waves. The basic subject matters of the book can be outlined as follows:

• exact absorbing conditions, the use of which promote substantially solution of some general theoretical problems in the computational electrodynamics (Chapters II–V);

• spatial-temporal and spatial-frequency electromagnetic field transformations under resonant conditions (Chapters VI–X).

The well-known heuristic and approximate methods of transition to bounded analysis domains in open time-domain problems are grounded basically on the use of the so-called Absorbing Boundary Conditions (ABCs) and Perfectly Matched Layers (PMLs). The essential disadvantage of these solutions is an unpredictable behavior of computational errors for large observation times and, as a consequence, the lack of reliable data for resonant wave scattering.

The approach developed in the book allows one to estimate and minimize the errors arising from the replacement of open initial boundary-value problems by closed problems. This technique is based on the construction and subsequent incorporation into a finite-difference scheme of the exact absorbing conditions, whose addition to the original initial boundary-value problem in no way affect the solution. The history of the issue can be briefly outlined as follows. In 1986, A.R. Maykov, A.G. Sveshnikov, and S.A. Yakunin were the first to formulate exact nonlocal conditions for virtual boundaries in cross-sections of regular semi-infinite hollow waveguides being the channels along which the signals generated by a waveguide unit propagate. Subsequently, their approach, being based on the use of the radiation conditions for space-time partial amplitudes (modes) of nonsine waves outgoing from the region where efficient sources and scatterers are located, was modified and developed as applied to various problems of theoretical and applied radio physics. The waveguide and antenna problems are considered as well as the analysis and synthesis of quasi-optical open dispersive resonators, the wave propagation in the surrounding environment, and other problems. For a number of special cases, the problems associated with a nonlocality and corner points (the intersection points for virtual coordinate boundaries) have been solved rigorously. The efficiency and correctness of the approach are confirmed by numerical experiments and test problems.

The analytical results of the work (Sections II–V: nonlocal and local exact absorbing conditions for various structures in various systems of coordinates; solution algorithms for the far-field zone problem and the problem of large and remote sources; a space-time analogue of the generalized scattering matrix method, etc.) are oriented to the use in the finite-difference computational schemes. The actual history and theory of this method is undoubtedly richer than those concise and simplified versions that are given in the electromagnetic community editions. The finite-difference time-domain method (FDTD-method), making its appearance in 1966 (see canonical paper of K.S. Yee), initiated the beginning of the computational boom. This method provides an example of a well thought-out realization of the known principles when discretizing the Maxwell curl equations. However, paper of K.S. Yee has not initiated an avalanche of the results, as is often claimed. It would be more properly to say that this paper has provided a substantial increase in the number of researchers being able to handle this method competently and to make the most efficient use of up-to-date computers when obtaining electrodynamic data. Unfortunately, a number of serious works on the theory of finite-difference methods and conception of their use in the applied mathematics and computational physics are referred to in none of the reviews dedicated to the FDTD-method.

J.L. Volakis and D.B. Davidson, the editors of the EM Programmer’s Notebook section in the Antennas & Propagation Magazine, describe the FDTD-method as ‘one of the workhorses of computational electromagnetics’. These words are certainly the recognition of the reliability and utility value of the approach, although in practice it performs, most often, only routine computational work. At the same time, a well-prepared numerical experiment turns the finite-difference algorithms into a universal, efficient, and rather fine tool for gaining new information on the physics of transient and steady-state processes. The conclusive five chapters of the book are devoted to the justification of this statement. The most interesting results of these chapters are as follows.

• A new approach to the analysis of spectral characteristics of open compact, waveguide, and periodic resonators by the time-domain methods has been developed and realized (Chapter VI).

• Slot resonances (half-wave and quarter-wave resonances on TEM-waves in narrow radial and coaxial slots of perfect conductors) were studied in detail for the first time by the rigorous time-domain methods. The excitation of the resonances of this kind changes substantially general properties of ordinary axially-symmetrical waveguide units and omnidirectional antennas of standard configuration (Chapters VII and VIII).

• The data on basic electrodynamic characteristics (amplitude-frequency and pulse response) of canonical axially-symmetrical radiators (monopoles, mirror and resonant antennas) are widely presented for the first time thus starting creation of the ‘library of elementary radiators’, which can simplify and accelerate solution of many applied problems (Chapter VIII).

• In the context of two-dimensional models, open electrodynamic structures (radiators operating on the effect of surface-into-bulk-wave transformation, ultra wide-band and resonant antennas, resonators with a substantially sparse spectrum, etc.) have been analyzed. Each structure may be considered as a prototype in the model synthesis of new devices of resonant quasi-optics, antenna engineering, vacuum and solid-state electronics (Chapter IX).

• Special and applied problems associated with the analysis and synthesis of resonant radiators of short high-power radio pulses, energy compressors, phased antenna arrays, and so on, have been solved (Chapter X).

The authors hope that the reader will find that the discussed physical and applied results are presented in an illuminating way. Thus, for example, some figures in Chapters 7 to 10 are accompanied by .exe-files which enable to watch in dynamics the space-time transformations of the electromagnetic field close to studied resonance structures. The archive with these files is open for downloading at http://www.ire.kharkov.ua/downloads/Book_Files.rar