Inverse Problems and Inverse Scattering of Plane Waves

Name: Inverse Problems and Inverse Scattering of Plane Waves
Brand: Academic Press
Price: 74.95 EUR
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Roy Ghosh Dilip N. Ghosh Roy L. S. Couchman(Autor*in)

Academic Press

Erschienen am 14. Mai 2014

339 Seiten

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978-0-08-054613-1 (ISBN)

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Inhalt

Front Cover
Inverse Problems and Inverse Scattering of Plane Waves
Contents
Chapter 1. Introduction
1.1 Direct and Inverse Problems
1.2 The Basic Concepts
Chapter 2. Some Examples of Ill-posed Problems
2.1 Introduction
2.2 Examples
Chapter 3. Theory of Ill-posed Problems
3.1 Introduction
3.2 Tikhonov's Theorem
3.3 Regularization on a Compactum: The Quasisolution
3.4 Generalized Solutions
3.5 Singular Value Expansion
3.6 Tikhonov's Theory of Regularization
3.7 Convergence, Stability and Optimality
3.8 The Determination of a
3.9 An Application
3.10 The Method of Mollification
Chapter 4. Regularization by Projections
4.1 Introduction
4.2 The Basic Projection Methods
4.3 The Method of Projections: General Framework
4.4 The Method of Least-Square
4.5 The Method of Collocation
4.6 The Standard Galerkin Method
Chapter 5. Discrete Ill-posed Problems
5.1 Introduction
5.2 Discrete Decompositions
5.3 The Discrete Tikhonov Regularization
5.4 An Example
5.5 Discrete Solution of a Tikhonov Functional
5.6 Appendix A.5.1
5.7 Appendix A.5.2
5.8 Appendix A.5.3
Chapter 6. The Helmholtz Scattering
6.1 Introduction
6.2 Gauss' or Divergence Theorem
6.3 Green's Identities
6.4 The Helmholtz Equation
6.5 The Helmholtz Representation in the Interior
6.6 The Radiation Condition
6.7 The Helmholtz Representation in the Exterior
6.8 Some Properties of the Scattering Solutions
6.9 The Helmholtz Scattering from Inhomogeneities
Chapter 7. The Solutions
7.1 Introduction
7.2 The Layer Potentials
7.3 Replacing G0(x, y
k) by g0(x, y).
7.4 The Double-layer Potential
7.5 The Single-layer Potential
7.6 The Helmholtz Scattering Problems
7.7 Unconditionally Unique Solution
7.8 The Transmission Problem
7.9 Jones' Method
7.10 Appendix A.7.1
7.11 Appendix A.7.2
7.12 Appendix A.7.3
7.13 Appendix A.7.4
7.14 Appendix A.7.5
7.15 Appendix A.7.6
Chapter 8. Uniqueness Theorems in Inverse Problems
8.1 Some Definitions
8.2 Properties of the Total Fields
8.3 The Dirichlet and Neumann Spectrum
8.4 The Uniqueness of the Inverse Dirichlet Obstacle Problem
8.5 The Uniqueness of Inverse Neumann Obstacle
8.6 Uniqueness in Inverse Transmission Obstacle
8.7 Uniqueness of Inverse Inhomogeneity Scattering
8.8 Appendix A.8.1
8.9 Appendix A.8.2
Chapter 9. Some Algorithms
9.1 Introduction
9.2 The Method of Potentials
9.3 The Method of Superposition of Incident Fields
9.4 The Method of Wavefunction Expansion
9.5 The Method of Boundary Variation
9.6 Some Nonoptimizational Methods
9.7 Appendix A.9.1
9.8 Appendix A.9.2
9.9 Appendix A.9.3
Chapter 10. Bibliography

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