Problems of High Frequency Diffraction by Elongated Bodies

The book discusses why classical asymptotic expansions are not applicable to extremely elongated bodies and suggests a way out by defining a special class of asymptotic approximations that are uniform with respect to the rate of body elongation. It covers diffraction by bodies of elliptical shape and other shapes, and provides mathematical formulas for the Whittaker functions. The reference solutions enable the validation of new numerical solvers.

Format: Hardback
Length: 188 pages
Publication date: 15 April 2023
Publisher: Springer Verlag, Singapore

While classical asymptotic expansions provide a decent approximation for diffracted fields in general, they appear scarcely applicable to extremely elongated bodies. This presents challenges on both fronts: on the one hand, due to the large system size, numerical solvers find it exceedingly difficult to tackle these problems. On the other hand, describing these bodies using classical asymptotic methods becomes challenging.

The book delves into the reasons behind this phenomenon and offers a solution. By defining the characteristics of a strongly elongated body, it introduces a unique class of asymptotic approximations that are, in some sense, uniform with respect to the rate of body elongation.

Chapter 1 provides a concise overview of the results obtained by V. A. Fock and subsequent advancements in his approach to diffraction by elongated obstacles. It outlines the cases of moderately and strongly elongated bodies. The remainder of the book details the approach of special parabolic equations, which lead to new asymptotic approximations for the diffracted fields. Chapters 2, 3, and 4 focus on diffraction by bodies of elliptical shape: the elliptic cylinder with a strongly elongated cross section and the prolate spheroid with a high aspect ratio. Chapter 5 extends the approach to other shapes such as narrow cones and narrow hyperboloids. The mathematical formulas for the Whittaker functions, widely used throughout the book, are compiled in the Appendix.

The concise derivations are accompanied by numerous test examples that compare asymptotic approximations with numerically computed fields, elucidating the intricacies of high-frequency diffraction by strongly elongated bodies. The reference solutions presented in the book enable the validation of newly developed numerical solvers.

Weight: 471g
Dimension: 235 x 155 (mm)
ISBN-13: 9789819912759
Edition number: 1st ed. 2023