Inverse problems and inverse scattering of plane waves / D.N. Ghosh Roy, L.S. Couchman.

Format:

Book

Author/Creator:

Ghosh Roy, Dilip N., 1939-

Contributor:

Couchman, L. S.

Language:

English

Subjects (All):

Scattering (Physics).

Inverse scattering transform.

Sound.

Physical Description:

1 online resource (339 p.)

Place of Publication:

San Diego : Academic Press, c2002.

Language Note:

English

Summary:

The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas

Contents:

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 Projections4.1 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 Identities6.4 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.7.27.12 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 Fields9.4 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

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 315-330) and index.

ISBN:

1-281-03710-9

9786611037109

0-08-054613-7

OCLC:

476077265