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Parabolic equation methods for electromagnetic wave propagation. (English) Zbl 0943.78001

IEE Electromagnetic Waves Series. 45. London: IEE, The Institution of Electrical Engineers. x, 336 p. (2000).
This book is number 45 of the electromagnetic wave series of the Institute of Electrical Engineers. It opens with a short chapter giving a potted history of the subject. In the second chapter, entitled the ‘Parabolic equation framework’, the author discusses the fundamental equation of the subject, introducing topics such as the expression of the properties of the system in terms of pseudodifferential operators and approximations of the square root operator. In the third chapter, on parallel equation algorithms, she passes on to the use of techniques such as the split-step sine transform and finite-difference implementation of the parabolic equation. The fourth chapter deals with tropospheric radiowave propagation and introduces the concept of earth flattening transformations and indicates how boundary conditions can be modified. Also discussed is the concept of path loss.
The fifth chapter is entitled ‘Rays and modes’ and gives an account of the methods of ray tracing and of mode theory. This leads on to the next chapter, on oversea propagation where the importance of ducts is discussed. Following on this there is a chapter on irregular terrain modelling when amongst the covered topics are diffraction by the earth, knife edge diffraction and the use of conformal mapping. The eighth chapter deals with domain truncation, introducing the concepts of absorbing and perfectly matched layers, and nonlocal boundary conditions.
In the ninth chapter on impedance boundary modelling the author introduces the application of the Leontovich boundary condition and points out the different effects of very dry ground, dry ground and sea. The recovery effect occurring at the land sea boundary is also discussed. The following chapter is concerned with propagation over a rough sea surface. The concept of rough sea impedance is discussed together with ducting propagation. The eleventh chapter is on the so-called hybrid methods. In this, the author indicates which methods may be useful under various conditions. Amongst the treated topics are physical optics, spectral decomposition, high antennas and Earth-space radio links.
The next two chapters are concerned with two- and three-dimensional scattering, respectively. Padé approximations are introduced in a variety of forms, an application to X-ray optics is discussed, suggestions for rough surfaces models are treated and there is a mention of building scatterers. The final chapter is on vector parabolic equations with discussions of testing scattering algorithms by means of calculating some radar cross sections, for example the “NASA Almond”. Four appendices follow, dealing with Airy functions, far-field expressions, the theoretical derivation of mode series and energy conservation. The book ends with a list of 176 references, the latest being 1999.
This is an interesting work. It contains a great deal which will be of interest to those working in this field, although in some ways it falls between two stools, it seems to lie halfway between a textbook and a reference book, as in some places finite difference approximations are provided for partial differential equations and in other there are no such hints for numerical solutions. In one or two places statements are made but no indication is given as to how they are arrived at (e.g. equations 3.97 and 4.55). On the whole however, the book is well written and it can be recommended.

MSC:

78-02 Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
78A45 Diffraction, scattering
35K20 Initial-boundary value problems for second-order parabolic equations
78M25 Numerical methods in optics (MSC2010)
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