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The Linear Sampling Method in Inverse Electromagnetic Scattering

2011-01-01 Mathematics
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Release : 2011-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 402/5 ( reviews)

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Book Synopsis The Linear Sampling Method in Inverse Electromagnetic Scattering by : Fioralba Cakoni

Download or read book The Linear Sampling Method in Inverse Electromagnetic Scattering written by Fioralba Cakoni. This book was released on 2011-01-01. Available in PDF, EPUB and Kindle. Book excerpt: The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation's solution as an indicator function for the determination of the support of the scattering object. This book describes the linear sampling method for a variety of electromagnetic scattering problems. It presents uniqueness theorems and the derivation of various inequalities on the material properties of the scattering object from a knowledge of the far field pattern of the scattered wave.

Inverse Acoustic and Electromagnetic Scattering Theory

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 352/5 ( reviews)

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Book Synopsis Inverse Acoustic and Electromagnetic Scattering Theory by : David Colton

Download or read book Inverse Acoustic and Electromagnetic Scattering Theory written by David Colton. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: It has now been almost ten years since our first book on scattering theory ap peared [32]. At that time we claimed that "in recent years the development of integral equation methods for the direct scattering problem seems to be nearing completion, whereas the use of such an approach to study the inverse scattering problem has progressed to an extent that a 'state of the art' survey appears highly desirable". Since we wrote these words, the inverse scattering problem for acoustic and electromagnetic waves has grown from being a few theoreti cal considerations with limited numerical implementations to a weH developed mathematical theory with tested numerical algorithms. This maturing of the field of inverse scattering theory has been based on the realization that such problems are in general not only nonlinear but also improperly posed in the sense that the solution does not depend continuously on the measured data. This was emphasized in [32] and treated with the ideas and tools available at that time. Now, almost ten years later, these initial ideas have developed to the extent that a monograph summarizing the mathematical basis of the field seems appropriate. This book is oUf attempt to write such a monograph. The inverse scattering problem for acoustic and electromagnetic waves can broadly be divided into two classes, the inverse obstacle problem and the inverse medium problem.

Inverse Acoustic and Electromagnetic Scattering Theory

2019-11-06 Mathematics
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Release : 2019-11-06
Genre : Mathematics
Kind : eBook
Book Rating : 519/5 ( reviews)

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Book Synopsis Inverse Acoustic and Electromagnetic Scattering Theory by : David Colton

Download or read book Inverse Acoustic and Electromagnetic Scattering Theory written by David Colton. This book was released on 2019-11-06. Available in PDF, EPUB and Kindle. Book excerpt: The inverse scattering problem is central to many areas of science and technology such as radar, 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. In this fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions. Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added.

Qualitative Methods in Inverse Scattering Theory

2005-12-29 Mathematics
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Release : 2005-12-29
Genre : Mathematics
Kind : eBook
Book Rating : 307/5 ( reviews)

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Book Synopsis Qualitative Methods in Inverse Scattering Theory by : Fioralba Cakoni

Download or read book Qualitative Methods in Inverse Scattering Theory written by Fioralba Cakoni. This book was released on 2005-12-29. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years. The increasing demands of imaging and target identification require new powerful and flexible techniques besides the existing weak scattering approximation or nonlinear optimization methods. One class of such methods comes under the general description of qualitative methods in inverse scattering theory. This textbook is an easily-accessible "class-tested" introduction to the field. It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.

DIRECT SAMPLING METHODS FOR INVERSE SCATTERING PROBLEMS

2017
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Release : 2017
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Book Synopsis DIRECT SAMPLING METHODS FOR INVERSE SCATTERING PROBLEMS by :

Download or read book DIRECT SAMPLING METHODS FOR INVERSE SCATTERING PROBLEMS written by . This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: Abstract : Recently, direct sampling methods became popular for solving inverse scattering problems to estimate the shape of the scattering object. They provide a simple tool to directly reconstruct the shape of the unknown scatterer. These methods are based on choosing an appropriate indicator function f on Rd, d=2 or 3, such that f(z) decides whether z lies inside or outside the scatterer. Consequently, we can determine the location and the shape of the unknown scatterer. In this thesis, we first present some sampling methods for shape reconstruction in inverse scattering problems. These methods, which are described in Chapter 1, include Multiple Signal Classification (MUSIC) by Devaney, the Linear Sampling Method (LSM) by Colton and Kirsch, the Factorization Method by Kirsch, and the Direct Sampling Method by Ito et al. In Chapter 2, we introduce some direct sampling methods, including Orthogonality Sampling by Potthast and a direct sampling method using far field measurements for shape reconstruction by Liu. In Chapter 3, we generalize Liu's method for shape reconstruction in inverse electromagnetic scattering problems. The method applies in an inhomogeneous isotropic medium in R3 and uses the far field measurements. We study the behavior of the new indicator for the sampling points both outside and inside the scatterer. In Chapter 4, we propose a new sampling method for multifrequency inverse source problem for time-harmonic acoustics using a finite set of far field data. We study the theoretical foundation of the proposed sampling method, and present some numerical experiments to demonstrate the feasibility and effectiveness of the method. Final conclusions of this thesis are summarized in Chapter 5. Recommendations for possible future works are also given in this chapter.

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