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Inverse acoustic and electromagnetic scattering theory相反音响和电磁式驱散的理论

Inverse acoustic and electromagnetic scattering theory相反音响和电磁式驱散的理论

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作者: Rainer Kress 著 , David Colton

出版社: 广东教育出版社

出版时间: 1998-01

版次: 1

ISBN: 9783540628385

定价: 1056.00

装帧: 精装

开本: 16开

纸张: 胶版纸

页数: 334页

分类: 外文古旧书>英文书>工程技术

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. 1  Introduction

    1.1  The Direct Scattering Problem

    1.2  The Inverse Scattering Problem

2  The Hetmholtz Equation

    2.1  Acoustic Waves

    2.2  Green's Theorem and Formula

    2.3  Spherical Harmonics

    2.4  Spherical Bessel Functions

    2.5  The Far Field Mapping

3  Direct Acoustic Obstacle Scattering

    3.1  Single- and Double-Layer Potentials

    3.2  Scattering from a Sound-Soft Obstacle

    3.3  The Reciprocity Relation

    3.4  The Two-Dimensional Case

    3.5  On the Numerical Solution in IR2

    3.6  On the Numerical Solution in IR3

4  Ill-Posed Problems

    4.1  The Concept of Ill-Posedness

    4.2  Regularization Methods

    4.3  Singular Value Decomposition

    4.4  Tikhonov Regularization

    4.5  Nonlinear Operators

5  Inverse Acoustic Obstacle Scattering

    5.1  Uniqueness

    5.2  Physical Optics Approximation

    5.3  Continuity and Differentiability of the Far Field Mapping

    5.4  Approximation of the Scattered Field

    5.5  Superposition of the Incident Fields

6  The Maxwell Equations

    6.1  Electromagnetic Waves

    6.2  Green's Theorem and Formula

    6.3  Vector Potentials

    6.4  Scattering from a Perfect Conductor

    6.5  Vector Wave Functions

    6.6  The Reciprocity Relation

7  Inverse Electromagnetic Obstacle Scattering

    7.1  Uniqueness

    7.2  Continuous Dependence on the Boundary

    7.3  Approximation of the Scattered Field

    7.4  Superposition of the Incident Fields

8  Acoustic Waves in an Inhomogeneous Medium

    8.1  Physical Background

    8.2  The Lippmann-Schwinger Equation

    8.3  The Unique Continuation Principle

    8.4  Far Field Patterns

    8.5  The Analytic Fredholm Theory

    8.6  Transmission Eigenvalues

    8.7  Numerical Methods

9  Electromagnetic Waves in an Inhomogeneous Medium

    9.1  Physical Background

    9.2  Existence and Uniqueness

    9.3  Far Field Patterns

    9.4  The Spherically Stratified Dielectric Medium

    9.5  The Exterior Impedance Boundary Value Problem

10  The Inverse Medium Problem

    10.1 The Inverse Medium Problem for Acoustic Waves

    10.2 A Uniqueness Theorem

    10.3 A Dual Space Method

    10.4 A Modified Dual Space Method

    10.5 The Inverse Medium Problem for Electromagnetic Waves

    10.6 Numerical Examples

    10.7 The Two-Dimensional Case

References

Index
内容简介:
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.
目录:
1  Introduction

    1.1  The Direct Scattering Problem

    1.2  The Inverse Scattering Problem

2  The Hetmholtz Equation

    2.1  Acoustic Waves

    2.2  Green's Theorem and Formula

    2.3  Spherical Harmonics

    2.4  Spherical Bessel Functions

    2.5  The Far Field Mapping

3  Direct Acoustic Obstacle Scattering

    3.1  Single- and Double-Layer Potentials

    3.2  Scattering from a Sound-Soft Obstacle

    3.3  The Reciprocity Relation

    3.4  The Two-Dimensional Case

    3.5  On the Numerical Solution in IR2

    3.6  On the Numerical Solution in IR3

4  Ill-Posed Problems

    4.1  The Concept of Ill-Posedness

    4.2  Regularization Methods

    4.3  Singular Value Decomposition

    4.4  Tikhonov Regularization

    4.5  Nonlinear Operators

5  Inverse Acoustic Obstacle Scattering

    5.1  Uniqueness

    5.2  Physical Optics Approximation

    5.3  Continuity and Differentiability of the Far Field Mapping

    5.4  Approximation of the Scattered Field

    5.5  Superposition of the Incident Fields

6  The Maxwell Equations

    6.1  Electromagnetic Waves

    6.2  Green's Theorem and Formula

    6.3  Vector Potentials

    6.4  Scattering from a Perfect Conductor

    6.5  Vector Wave Functions

    6.6  The Reciprocity Relation

7  Inverse Electromagnetic Obstacle Scattering

    7.1  Uniqueness

    7.2  Continuous Dependence on the Boundary

    7.3  Approximation of the Scattered Field

    7.4  Superposition of the Incident Fields

8  Acoustic Waves in an Inhomogeneous Medium

    8.1  Physical Background

    8.2  The Lippmann-Schwinger Equation

    8.3  The Unique Continuation Principle

    8.4  Far Field Patterns

    8.5  The Analytic Fredholm Theory

    8.6  Transmission Eigenvalues

    8.7  Numerical Methods

9  Electromagnetic Waves in an Inhomogeneous Medium

    9.1  Physical Background

    9.2  Existence and Uniqueness

    9.3  Far Field Patterns

    9.4  The Spherically Stratified Dielectric Medium

    9.5  The Exterior Impedance Boundary Value Problem

10  The Inverse Medium Problem

    10.1 The Inverse Medium Problem for Acoustic Waves

    10.2 A Uniqueness Theorem

    10.3 A Dual Space Method

    10.4 A Modified Dual Space Method

    10.5 The Inverse Medium Problem for Electromagnetic Waves

    10.6 Numerical Examples

    10.7 The Two-Dimensional Case

References

Index

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