## Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles

Posted by Hamada Rageh on Friday, January 21, 2011

**P. A. Martin, "Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles" **

Cambridge University Press | 2006 | ISBN: 0521865549 | 450 pages | PDF | 1,5 MB

The interaction of waves with obstacles is an everyday phenomenon in
science and engineering, arising for example in acoustics,
electromagnetism, seismology and hydrodynamics. The mathematical theory
and technology needed to understand the phenomenon is known as multiple
scattering, and this book is the first devoted to the subject. The
author covers a variety of techniques, describing first the
single-obstacle methods and then extending them to the multiple-obstacle
case. A key ingredient in many of these extensions is an appropriate
addition theorem: a coherent, thorough exposition of these theorems is
given, and computational and numerical issues around them are explored.
The application of these methods to different types of problems is also
explained; in particular, sound waves, electromagnetic radiation, waves
in solids and water waves. A comprehensive bibliography of some 1400
items rounds off the book, which will be an essential reference on the
topic for applied mathematicians, physicists and engineers.

• Describes all the main methods for solving multiple scattering problems exactly, as well as the main approximate solution methods; gives thorough exposition of addition theorems • Contains many historical remarks and an extensive 1400-item bibliography • Covers the four main application areas of acoustics, elastodynamics, electromagnetics and hydrodynamics

Contents

Preface; 1. Introduction; 2. Addition theorems in two dimensions; 3. Addition theorems in three dimensions; 4. Methods based on separation of variables; 5. Integral equation methods I: basic theory; 6. Integral equation methods II: further details; 7. Null-field and T-matrix methods; 8. Approximations; Appendices; Comments on the bibliography; Bibliography; Citation index; Index.

Reviews

'… an impressive text that presents a catalogue of methods and techniques associated with the solution of a class of important problems emerging from the study of wave propagation in a range of physical applications.' Journal of Fluid Mechanics

'Martin's Multiple Scattering is a wonderful example of the unity brought about by mathematics across four different branches of classical physics: acoustics, elastodynamics, hydrodynamics, and electrodynamics. With its clear and illuminating derivations, excellent literature coverage, exposure of common and not-so-common pitfalls, indications of which parts of the field are mature and which are still in rapid development (e.g. fast multiple methods), and straightforward mention of open problems and suggestions for future research, I cannot recommend it too strongly. it is an excellent book.' Society for Industrial and Applied Mathematics Journal

' … can be recommended not only to specialists … but to anybody who enjoys reading classical books due to their clarity and self-consistency … suitable for engineers and applied scientists looking for a comprehensive introduction to the subject containing explicit recipes on how to attack the problem numerically.' American Mathematical Society

' … exemplary … is an absolute must for all Ph.D. students, researchers, and engineers specializing in any discipline dealing with wave scattering by composite objects and its applications. The book is written on the highest professional level and may serve as the basis of a lecture course on multiple wave scattering. The polygraphic quality of the book is impeccable and matches the quality of its contents.' Journal of Quantitative Spectroscopy & Radiative Transfer

' … an impressive text … this book will appeal to applied mathematicians, physicists and engineers with an interest in applications involving the linear theory of wave scattering … I found this a book easy to dip in and out of at odd moments, as well as rewarding to the reader making a more serious investment of their time.' Journal of Fluid Mechanics

' … no one interested in multiple scattering can afford to ignore Paul Martin's book.' Journal of Acoustical Society of America

• Describes all the main methods for solving multiple scattering problems exactly, as well as the main approximate solution methods; gives thorough exposition of addition theorems • Contains many historical remarks and an extensive 1400-item bibliography • Covers the four main application areas of acoustics, elastodynamics, electromagnetics and hydrodynamics

Contents

Preface; 1. Introduction; 2. Addition theorems in two dimensions; 3. Addition theorems in three dimensions; 4. Methods based on separation of variables; 5. Integral equation methods I: basic theory; 6. Integral equation methods II: further details; 7. Null-field and T-matrix methods; 8. Approximations; Appendices; Comments on the bibliography; Bibliography; Citation index; Index.

Reviews

'… an impressive text that presents a catalogue of methods and techniques associated with the solution of a class of important problems emerging from the study of wave propagation in a range of physical applications.' Journal of Fluid Mechanics

'Martin's Multiple Scattering is a wonderful example of the unity brought about by mathematics across four different branches of classical physics: acoustics, elastodynamics, hydrodynamics, and electrodynamics. With its clear and illuminating derivations, excellent literature coverage, exposure of common and not-so-common pitfalls, indications of which parts of the field are mature and which are still in rapid development (e.g. fast multiple methods), and straightforward mention of open problems and suggestions for future research, I cannot recommend it too strongly. it is an excellent book.' Society for Industrial and Applied Mathematics Journal

' … can be recommended not only to specialists … but to anybody who enjoys reading classical books due to their clarity and self-consistency … suitable for engineers and applied scientists looking for a comprehensive introduction to the subject containing explicit recipes on how to attack the problem numerically.' American Mathematical Society

' … exemplary … is an absolute must for all Ph.D. students, researchers, and engineers specializing in any discipline dealing with wave scattering by composite objects and its applications. The book is written on the highest professional level and may serve as the basis of a lecture course on multiple wave scattering. The polygraphic quality of the book is impeccable and matches the quality of its contents.' Journal of Quantitative Spectroscopy & Radiative Transfer

' … an impressive text … this book will appeal to applied mathematicians, physicists and engineers with an interest in applications involving the linear theory of wave scattering … I found this a book easy to dip in and out of at odd moments, as well as rewarding to the reader making a more serious investment of their time.' Journal of Fluid Mechanics

' … no one interested in multiple scattering can afford to ignore Paul Martin's book.' Journal of Acoustical Society of America