Inverse acoustic and electromagnetic scattering theory相反音響和電磁式驅(qū)散的理論

內(nèi)容概要

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.

書籍目錄

1  Introduction    1.1  The Direct Scattering Problem    1.2  The Inverse Scattering Problem2  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 Mapping3  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 IR34  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 Operators5  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 Fields6  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 Relation7  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 Fields8  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 Methods9  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 Problem10  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 CaseReferencesIndex

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