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Inverse acoustic and electromagnetic scattering theory / David Colton, Rainer Kress.

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Author/Creator:
Colton, David L., 1943-
Language:
English.
Publication date:
2013
Imprint:
3rd ed. - New York : Springer, 2013.
Format:
  • Book
  • xiv, 405 p. : ill. ; 25 cm.
Bibliography:
Includes bibliographical references and index.
Contents:
  • 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
  • References
  • Index.
Contributor:
Kress, Rainer, 1941-
Series:
Applied mathematical sciences, 0066-5452 ; v. 93
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 93.
Subjects:
ISBN:
9781461449416
1461449413

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