Time-Domain Scattering

The first thorough synthesis of methods for solving time-domain scattering problems, covering both theoretical and computational aspects.

P. A. Martin (Author)

9781108835596, Cambridge University Press

Hardback, published 24 June 2021

267 pages
23.4 x 15.6 x 1.9 cm, 0.588 kg

'The book under review is very interesting and appealing to anyone who is interested in time-domain wave scattering. It is also a very useful and comprehensive book, with 910 references; I strongly recommend it to students and researchers who are working on time-domain scattering or inverse scattering problems. There are a lot of concrete examples, with emphasis placed on exact methods, such as separation of variables, and boundary integral equations. This makes the book easy to understand, and very friendly to readers.' Hongpeng Sun, MathSciNet

The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of applications. This book explains clearly the fundamental ideas of time-domain scattering, including in-depth discussions of separation of variables and integral equations. The author covers both theoretical and computational aspects, and describes applications coming from acoustics (sound waves), elastodynamics (waves in solids), electromagnetics (Maxwell's equations) and hydrodynamics (water waves). The detailed bibliography of papers and books from the last 100 years cement the position of this work as an essential reference on the topic for applied mathematicians, physicists and engineers.

1. Acoustics and the Wave Equation
2. Wavefunctions
3. Characteristics and Discontinuities
4. Initial-boundary Value Problems
5. Use of Laplace Transforms
6. Problems with Spherical Symmetry
7. Scattering by a Sphere
8. Scattering Frequencies and the Singularity Expansion Method
9. Integral Representations
10. Integral Equations
References
Citation Index
Index.

Subject Areas: Acoustic & sound engineering [TTA], Wave mechanics [vibration & acoustics PHDS], Fluid mechanics [PHDF], Mathematical modelling [PBWH], Differential calculus & equations [PBKJ]