Inverse Acoustic and Electromagnetic Scattering Theory

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Springer Science & Business Media, Oct 26, 2012 - Mathematics - 406 pages

The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scattering theory.

Review of earlier editions:

“Colton and Kress have written a scholarly, state of the art account of their view of direct and inverse scattering. The book is a pleasure to read as a graduate text or to dip into at leisure. It suggests a number of open problems and will be a source of inspiration for many years to come.”

SIAM Review, September 1994

“This book should be on the desk of any researcher, any student, any teacher interested in scattering theory.”

Mathematical Intelligencer, June 1994


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Chapter 1 Introduction
Chapter 2 The Helmholtz Equation
Chapter 3 Direct Acoustic Obstacle Scattering
Chapter 4 IllPosed Problems
Chapter 5 Inverse Acoustic Obstacle Scattering
Chapter 6 The Maxwell Equations
Chapter 7 Inverse Electromagnetic Obstacle Scattering
Chapter 8 Acoustic Waves in an Inhomogeneous Medium
Chapter 9 Electromagnetic Waves in an Inhomogeneous Medium
Chapter 10 The Inverse Medium Problem

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About the author (2012)

Rainer Kress is a Full Professor of Numerical and Applied Mathematics at the University of Gottingen. He has been a member of the Gottingen Academy of Sciences since 1995 and Professor Emeritus since 2010. He is the author or coauthor of five books.