Results 1  10
of
20
The determination of boundary coefficients from far field measurements
"... Dedicated to Chuck Groetsch for his fundamental contributions to the field of inverse problems. We consider the problem of determining either the surface impedance λ = λ(x) or surface conductivity η = η(x) from far field data corresponding to timeharmonic incident plane waves scattered by a coated ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
Dedicated to Chuck Groetsch for his fundamental contributions to the field of inverse problems. We consider the problem of determining either the surface impedance λ = λ(x) or surface conductivity η = η(x) from far field data corresponding to timeharmonic incident plane waves scattered by a coated infinite cylinder. We show that λ and η are uniquely determined from the far field data and provide a numerical algorithm for determining these quantities. 1
Open problems in the qualitative approach to inverse electromagnetic scattering theory
 European Jour. Applied Math
"... We formulate a number of open problems for timeharmonic inverse electromagnetic scattering theory focusing on uniqueness theorems, the determination of the support of a scattering object and the determination of material parameters 1 ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
We formulate a number of open problems for timeharmonic inverse electromagnetic scattering theory focusing on uniqueness theorems, the determination of the support of a scattering object and the determination of material parameters 1
Recent developments in the qualitative approach to inverse scattering theory
 12:1 WSPC/Trim Size: 9in x 6in for Proceedings CakoniGreece05
"... We consider the inverse scattering problem of determining both the shape and some of the physical properties of the scattering object from a knowledge of the (measured) electric and magnetic fields due to the scattering of an incident time harmonic electromagnetic wave at fixed frequency. We shall d ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
We consider the inverse scattering problem of determining both the shape and some of the physical properties of the scattering object from a knowledge of the (measured) electric and magnetic fields due to the scattering of an incident time harmonic electromagnetic wave at fixed frequency. We shall discuss the linear sampling method for solving the inverse scattering problem which does not require any a priori knowledge of the geometry and the physical properties of the scatterer. Included in our discussion is the case of partially coated objects and inhomogeneous background. We give references for numerical examples for each problem discussed in this paper. Key words: Electromagnetic inverse scattering, inverse scattering problem, linear sampling method, mixed boundary value problem. 1
A SPECTRALELEMENT METHOD FOR TRANSMISSION EIGENVALUE PROBLEMS ⋆
"... Abstract. We develop an efficient spectralelement method for computing the transmission eigenvalues in twodimensional radially stratified media. Our method is based on a dimension reduction approach which reduces the problem to a sequence of onedimensional eigenvalue problems that can be efficien ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We develop an efficient spectralelement method for computing the transmission eigenvalues in twodimensional radially stratified media. Our method is based on a dimension reduction approach which reduces the problem to a sequence of onedimensional eigenvalue problems that can be efficiently solved by a spectralelement method. We provide an error analysis which shows that the convergence rate of the eigenvalues is twice that of the eigenfunctions in energy norm. We present ample numerical results to show that the method convergences exponentially fast for piecewise stratified media, and is very effective, particularly for computing the few smallest eigenvalues. 1.
Inequalities in Inverse Scattering Theory
 J. of Inverse and Illposed Problems
"... Abstract. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous dielectric medium that is partially coated by a thin metallic layer in R 2. We use far field pattern of the scattered waves at a fixed frequency as data to determine the support D of the inh ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous dielectric medium that is partially coated by a thin metallic layer in R 2. We use far field pattern of the scattered waves at a fixed frequency as data to determine the support D of the inhomogeneous obstacle, the surface conductivity that characterizes the coating and the relative permittivity. No a prior information on the material properties of the scatterer is needed. The support D is determined by the linear sampling method which is based on the approximate solution of the far field equation. This solution is also used to obtain lower bounds for the surface conductivity and relative permittivity. The techniques for solving this inverse scattering problem rely on the analysis of a non standard boundary value problem known as the interior transmission problem. Key words. Inverse scattering problem, inhomogeneous medium, interior transmission problem, electromagnetic waves, mixed boundary value problems, qualitative approaches in inverse scattering. AMS classification. 35P25, 35R30, 78A45. 1.
MIXED BOUNDARY VALUE PROBLEMS IN INVERSE ELECTROMAGNETIC SCATTERING ∗
"... We consider the scattering of time harmonic incident plane waves by partially coated perfect conductors and screens (including the case of no coating, i.e. the scatterer is a perfect conductor). Of particular interest to us is the inverse problem of determining the shape of surface impedance from a ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We consider the scattering of time harmonic incident plane waves by partially coated perfect conductors and screens (including the case of no coating, i.e. the scatterer is a perfect conductor). Of particular interest to us is the inverse problem of determining the shape of surface impedance from a knowledge of the far field pattern of the electric field. Our analysis is based on a study of mixed boundary value problems for Maxwell’s equations. 1.
Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction
, 2014
"... Abstract. An important step in estimating the index of refraction of electromagnetic scattering problems is to compute the associated transmission eigenvalue problem. We develop in this paper efficient and accurate spectral methods for computing the transmission eigenvalues associated to the electro ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. An important step in estimating the index of refraction of electromagnetic scattering problems is to compute the associated transmission eigenvalue problem. We develop in this paper efficient and accurate spectral methods for computing the transmission eigenvalues associated to the electromagnetic scattering problems. We present ample numerical results to show that our methods are very effective for computing transmission eigenvalues (particularly for computing the smallest eigenvalue), and together with the linear sampling method, provide an efficient way to estimate the index of refraction of a nonabsorbing inhomogeneous medium. AMS subject classifications: 78A45, 65N35, 35J05, 41A58 Key words: spectral method, index of refraction, transmission eigenvalue, electromagnetic scat
SPECTRAL APPROXIMATION TO A TRANSMISSION EIGENVALUE PROBLEM AND ITS APPLICATIONS TO AN INVERSE PROBLEM
"... Abstract. We first develop an efficient spectralGalerkin method and an rigorous error analysis for the generalized eigenvalue problems associated to a transmission eigenvalue problem. Then, we present an iterative scheme, based on computation of the first transmission eigenvalue, to estimate the ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We first develop an efficient spectralGalerkin method and an rigorous error analysis for the generalized eigenvalue problems associated to a transmission eigenvalue problem. Then, we present an iterative scheme, based on computation of the first transmission eigenvalue, to estimate the index of refraction of an inhomogeneous medium. We present ample numerical results to demonstrate the effectiveness and accuracy of our approach. 1.
Inside Out II MSRI Publications
"... Transmission eigenvalues in inverse scattering theory FIORALBA CAKONI AND HOUSSEM HADDAR In the past few years transmission eigenvalues have become an important area of research in inverse scattering theory with active research being undertaken in many parts of the world. Transmission eigenvalues ap ..."
Abstract
 Add to MetaCart
Transmission eigenvalues in inverse scattering theory FIORALBA CAKONI AND HOUSSEM HADDAR In the past few years transmission eigenvalues have become an important area of research in inverse scattering theory with active research being undertaken in many parts of the world. Transmission eigenvalues appear in the study of scattering by inhomogeneous media and are closely related to nonscattering waves. Such eigenvalues provide information about material properties of the scattering media and can be determined from scattering data. Hence they can play an important role in a variety of inverse problems in target identification and nondestructive testing. The transmission eigenvalue problem is a nonselfadjoint and nonlinear eigenvalue problem that is not covered by the standard theory of eigenvalue problems for elliptic operators. This article provides a comprehensive review of the stateofthe art theoretical results on the transmission eigenvalue problem including a discussion on fundamental questions such as existence and discreteness of transmission eigenvalues as well as Faber–Krahn type inequalities relating the first eigenvalue to material properties of inhomogeneous media. We begin our presentation by showing how the transmission eigenvalue problem appears in scattering theory and how transmission eigenvalues are determined from scattering data. Then we discuss the simple case of spherically stratified media where it is possible to obtain partial results on inverse spectral problems. In the case of more general inhomogeneous media we discuss the transmission eigenvalue problem for various types of media employing different mathematical techniques. We conclude our presentation with a list of open problems that in our opinion merit investigation. 1.