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El. knyga: Inverse Acoustic and Electromagnetic Scattering Theory

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  • Formatas: PDF+DRM
  • Serija: Applied Mathematical Sciences v. 93
  • Išleidimo metai: 09-Mar-2013
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783662035375
Kitos knygos pagal šią temą:
Inverse Acoustic and Electromagnetic Scattering TheoryDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Applied Mathematical Sciences v. 93
  • Išleidimo metai: 09-Mar-2013
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783662035375
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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. To this second edition the authors have added new material on Newton's method for the inverse obstacle problem, a new elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a presentation of a new method for determining the support of an inhomogeneous medium from far field data. In addition the text has been updated in various places.

This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. The second edition includes material on Newton's method for the inverse obstacle problem, an elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a method for determining the support of an inhomogeneous medium from far field data.

Daugiau informacijos

2nd edition
1 Introduction
1(12)
1.1 The Direct Scattering Problem
2(5)
1.2 The Inverse Scattering Problem
7(6)
2 The Helmholtz Equation
13(25)
2.1 Acoustic Waves
13(3)
2.2 Green's Theorem and Formula
16(5)
2.3 Spherical Harmonics
21(7)
2.4 Spherical Bessel Functions
28(4)
2.5 The Far Field Mapping
32(6)
3 Direct Acoustic Obstacle Scattering
38(47)
3.1 Single- and Double-Layer Potentials
39(7)
3.2 Scattering from a Sound-Soft Obstacle
46(8)
3.3 The Reciprocity Relation
54(10)
3.4 The Two-Dimensional Case
64(3)
3.5 On the Numerical Solution in IR(2)
67(11)
3.6 On the Numerical Solution in IR(3)
78(7)
4 Ill-Posed Problems
85(20)
4.1 The Concept of Ill-Posedness
86(1)
4.2 Regularization Methods
87(2)
4.3 Singular Value Decomposition
89(8)
4.4 Tikhonov Regularization
97(5)
4.5 Nonlinear Operators
102(3)
5 Inverse Acoustic Obstacle Scattering
105(48)
5.1 Uniqueness
106(7)
5.2 Physical Optics Approximation
113(1)
5.3 Continuity and Differentiability of the Far Field Mapping
114(20)
5.4 Approximation of the Scattered Field
134(11)
5.5 Superposition of the Incident Fields
145(8)
6 The Maxwell Equations
153(42)
6.1 Electromagnetic Waves
154(1)
6.2 Green's Theorem and Formula
155(10)
6.3 Vector Potentials
165(7)
6.4 Scattering from a Perfect Conductor
172(5)
6.5 Vector Wave Functions
177(8)
6.6 The Reciprocity Relation
185(10)
7 Inverse Electromagnetic Obstacle Scattering
195(16)
7.1 Uniqueness
195(4)
7.2 Continuous Dependence on the Boundary
199(4)
7.3 Approximation of the Scattered Field
203(3)
7.4 Superposition of the Incident Fields
206(5)
8 Acoustic Waves in an Inhomogeneous Medium
211(39)
8.1 Physical Background
212(2)
8.2 The Lippmann-Schwinger Equation
214(4)
8.3 The Unique Continuation Principle
218(4)
8.4 Far Field Patterns
222(11)
8.5 The Analytic Fredholm Theory
233(5)
8.6 Transmission Eigenvalues
238(8)
8.7 Numerical Methods
246(4)
9 Electromagnetic Waves in an Inhomogeneous Medium
250(21)
9.1 Physical Background
251(1)
9.2 Existence and Uniqueness
252(4)
9.3 Far Field Patterns
256(3)
9.4 The Spherically Stratified Dielectric Medium
259(5)
9.5 The Exterior Impedance Boundary Value Problem
264(7)
10 The Inverse Medium Problem
271(47)
10.1 The Inverse Medium Problem for Acoustic Waves
272(2)
10.2 A Uniqueness Theorem
274(6)
10.3 A Dual Space Method
280(5)
10.4 A Modified Dual Space Method
285(4)
10.5 The Inverse Medium Problem for Electromagnetic Waves
289(11)
10.6 Numerical Examples
300(7)
10.7 The Two-Dimensional Case
307(11)
References 318(14)
Index 332


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