The Far-Field Equations in Linear Elasticity — an Inversion Scheme

Gintides, Drossos; Kiriaki, K.

doi:10.1002/1521-4001(200105)81:5<305::aid-zamm305>3.0.co;2-t

Cited by 35 publications

(27 citation statements)

References 12 publications

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“…In [10] and [11] Colton and Monk apply a superposition method in order to solve the inverse acoustic scattering problem, while in [9] Colton and Kress apply this method for the electromagnetic case. Dassios and Rigou studied the superposition of incident dyadic fields for the elastic case [13,14] and Gintides and Kiriaki used superposition method in order to solve inverse scattering problems in the resonance region in linear elasticity [16]. In the present work we extend the superposition method for the case of electromagnetic fields in chiral media.…”

Section: Superposition Of Incident Electric Fieldsmentioning

confidence: 96%

“…Athanasiadis et al have studied electromagnetic scattering by a homogeneous chiral obstacle in a chiral environment in [3] and Athanasiadis and Kardasi in [4] define the Herglotz functions of Beltrami and electromagnetic fields in a chiral medium. Herglotz functions have been extensively used by Colton and Kress in [9], Dassios and Rigou in [14] and Gintides and Kiriaki in [16] in order to study the inverse scattering problem.…”

Section: Introductionmentioning

confidence: 99%

“…Dassios and Rigou in [14] use elastic Herglotz dyadics for the solution of the inverse scattering problem associated with the shape reconstruction of a three-dimensional (3-D), star shaped rigid scatterer in the theory of elasticity. Gintides and Kiriaki in [15,16] use the properties of elastic Herglotz dyadics in order to consider the far-field equations in linear elasticity for the rigid body and the cavity. The far-field operator for electromagnetic scattering by a homogeneous chiral obstacle in an achiral environment has been studied in [5].…”

Section: Introductionmentioning

confidence: 99%

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On the far-field operator for electromagnetic scattering in chiral media

Athanasiadis

Kardasi

2006

Applicable Analysis

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We consider time-harmonic electromagnetic waves propagating in a homogeneous threedimensional unbounded chiral medium where a perfect conductor has been immersed. Assuming that the incident electric field is a superposition of plane incident electric waves, the corresponding scattered field and the far-field pattern are expressed as the superposition of the scattered fields and the far-field patterns respectively. It is also proved that the sets of far-field patterns are complete if and only if there does not exist an eigenfunction to the interior perfect conductor problem that vanishes on the boundary of the scatterer which is an electric Herglotz field. The Left-Circularly Polarized and the Right-Circularly Polarized far-field operators are defined and studied and using them the electric far-field operator is defined too. The properties of the above operators and Herglotz functions are related to the solution of the interior perfect conductor boundary value problem.

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Section: Superposition Of Incident Electric Fieldsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the far-field operator for electromagnetic scattering in chiral media

Athanasiadis

Kardasi

2006

Applicable Analysis

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“…In [7,11,12] Colton and Monk apply a superposition method in order to solve the inverse acoustic scattering problem while in [10] Colton and Kress apply this method for the electromagnetic case. Dassios and Rigou studied the superposition of incident dyadic fields for the elastic case [15] and Gintides and Kiriaki used superposition method in order to solve inverse scattering problems in the resonance region in linear elasticity [16,17], (for dyadic fields in elasticity see also [6,13]). In the present work we extend superposition method for the case of dyadic electromagnetic fields in chiral media.…”

Section: Superposition Of Incident Dyadic Fieldsmentioning

confidence: 99%

“…More details about scalar Herglotz functions for acoustics and vector Herglotz functions for electromagnetic waves can be found in [10]. In elasticity Herglotz dyadics are used by Dassios and Rigou in [15] and Gintides and Kiriaki in [17]. The basic theory for Herglotz functions in chiral media is developed in [3] where we define Beltrami Herglotz functions and chiral Herglotz pairs for the vector case and in [5] where we define Beltrami Herglotz dyadics and dyadic electromagnetic Herglotz pairs.…”

Section: Introductionmentioning

confidence: 99%

Inverse electromagnetic scattering by a perfect conductor in a chiral environment

Athanasiadis¹,

Kardasi²

2008

Jiip

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In this paper electromagnetic Herglotz dyadics are used to develop a superposition method and apply it for the study of an inversion scheme for electromagnetic scattering in chiral media. The direct scattering problem for the perfect conductor is formulated and Beltrami Herglotz dyadics and dyadic electromagnetic Herglotz pairs are being used. Assuming that the incident electromagnetic field is produced by a superposition of plane incident waves, the scattered field and the corresponding far-field pattern are expressed as the superposition of the scattered fields and the corresponding to them far-field patterns respectively. Far-field operators are defined and studied and an integral equation is posed. The solvability of this equation is related to the solution of the interior perfect conductor boundary value problem. Finally, an inversion scheme is posed and a theorem for it's solvability is proved.

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Inverse scattering problem for a rigid scatterer or a cavity in elastodynamics

Gintides

Midrinos

2010

Z Angew Math Mech

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We consider the inverse scattering problem for the shape determination of a rigid scatterer or a cavity in a homogeneous and isotropic elastic medium. Both problems are formulated in R2 for time‐harmonic fields and longitudinal or transversal incident plane waves. Representation of the scattered field as a single‐ or a double‐layer potential, equivalently, leads to a system of two nonlinear integral equations for the density and the parametrization of the boundary. A detailed numerical implementation is presented for computing the corresponding solutions of both systems and numerical reconstructions are given to show the effectiveness of the method.

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The Far-Field Equations in Linear Elasticity — an Inversion Scheme

Cited by 35 publications

References 12 publications

On the far-field operator for electromagnetic scattering in chiral media

On the far-field operator for electromagnetic scattering in chiral media

Inverse electromagnetic scattering by a perfect conductor in a chiral environment

Inverse scattering problem for a rigid scatterer or a cavity in elastodynamics

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