Inverse acoustic and electromagnetic scattering theory
- Colton, David L., 1943-
- 3rd ed.
- New York : Springer, 2013.
- Physical description
- xiv, 405 p. : ill. ; 25 cm.
- Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 93.
QC243.3 .S3 C65 2013
- Unknown QC243.3 .S3 C65 2013
- Kress, Rainer, 1941-
- Includes bibliographical references and index.
- Introduction. The direct scattering problem ; The inverse scattering problem
- The Helmholtz equation. Acoustic waves ; Green's theorem and formula ; Spherical harmonics ; Spherical bessel functions ; The far field pattern
- Direct acoustic obstacle scattering. Single- and double-layer potentials ; Scattering from a sound-soft obstacle ; Herglotz wave functions and the far field operator ; The two-dimensional case ; On the numerical solution in IR² ; On the numerical solution in IR³
- Ill-posed problems. The concept of Ill-posedness ; Regularization methods ; Singular value decomposition ; Tikhonov regularization ; Nonlinear operators
- Inverse acoustic obstacle scattering. Uniqueness ; Physical optics approximation ; Continuity and differentiability of the far field mapping ; Iterative solution methods ; Decomposition methods ; Sampling methods
- The Maxwell equations. Electromagnetic waves ; Green's theorem and formula ; Vector potentials ; Scattering from a perfect conductor ; Vector wave functions ; Herglotz pairs and the far field operator
- Inverse electromagnetic obstacle scattering. Uniqueness ; Continuity and differentiability of the far field mapping ; Iterative solution methods ; Decomposition methods ; Sampling methods
- Acoustic waves in an inhomogeneous medium. Physical background ; The Lippmann-Schwinger equation ; The unique continuation principle ; The far field pattern ; The analytic Fredholm theory ; Transmission eigenvalues ; Numerical methods
- Electromagnetic waves in an inhomogeneous medium. Physical background ; Existence and uniqueness ; The far field patterns ; The spherically stratified dielectric medium ; The exterior impedance boundary value problem
- The inverse medium problem. The inverse medium problem for acoustic waves ; Uniqueness ; Iterative solution methods ; Decomposition methods ; Sampling methods and transmission eigenvalues ; The inverse medium problem for electromagnetic waves ; Numerical examples
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- Publication date
- David Colton, Rainer Kress.
- Applied mathematical sciences, 0066-5452 ; v. 93