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Antenna array

Complex directional antenna consists of separate near-omnidirectional antennas (radiating elements) positioned in the space and driven by high-frequency …

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## Analytical techniques in the theory of guided waves

Published: 09/02/2009
Language: russian

Strict analytical methods of solving boundary value problems take a special place in mathematical physics. Although they can be applied to a comparatively narrow range of model problems, solutions obtained with their help are of great value because they can be used as a reliable basis for developing numerical and approximate calculation methods.

This book is basically devoted to the description and generalization of the two widespread analytical method of solving boundary value problems in mathematical physics. One of them — factorization method — became popular not so long ago and is successfully used to find the precise solution of important and interesting boundary value problems in electrodynamics, acoustics and the theory of elastic waves. Currently, the range of problems that can be solved with this method in its regular form is considerably exhausted. Though the second method — the partial domain method, which makes it possible to solve boundary value problems for complex domains consisting of plain subdomains — is widely used, obviously it is not completely theoretically based. In particular, until the recent time there had been no clear recommendations regarding the numerical solution of infinite systems of algebraic equations the formulation of the boundary value problem with the help of the method of crossing leads to.

The book by R. Mittra and S. Lee quite thoroughly describes both methods and it pays special attention to discovering the “points of contact” for these methods. The peculiarity of this book comes down to the detailed analysis of finding the solution for a small number of key problems, such as the waveguide junction problem or the problem of periodic structure consisting of parallel half–planes. Solving one and the same boundary value problem with different methods allows the authors to compare their advantages. A lot of instructive and sometimes practically interesting problems showing how to apply the described methods are given as appendices to the main text.

Taking the classic Wiener–Hopf functional equations and infinite systems of algebraic equations allowing the solution of a boundary value problem in the analytical form to be built are used as a basis for the generalization of both methods. The practical problems of electrodynamics that were solved in the authors' original works and by means of the modified residual methods and the modified Wiener–Hopf method are more realistic and interesting. Many of them are described in the book. However, it should be mentioned that the authors' main aim is not to solve particular problems, but to study and develop constructive methods for solving boundary value problems in electrodynamics.

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