The Development of New Methods for Solving the Target Identification or Inverse Scattering Problem for Time-Harmonic Acoustic and Electromagnetic Waves.

1984 ◽  
Author(s):  
D. L. Colton
Keyword(s):  
Inverse Scattering ◽  
Electromagnetic Waves ◽  
Target Identification ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
New Methods ◽  
Time Harmonic

The electromagnetic inverse-scattering problem for partly coated Lipschitz domains

2004 ◽  
Vol 134 (4) ◽  
pp. 661-682 ◽  
Author(s):  
Fioralba Cakoni ◽  
David Colton ◽  
Peter Monk
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattered Wave ◽  
Field Pattern ◽  
Electromagnetic Plane Wave ◽  
Linear Sampling Method ◽  
Time Harmonic ◽  
Far Field Pattern ◽  
Electromagnetic Plane

We consider the inverse-scattering problem of determining the shape of a partly coated obstacle in R3 from a knowledge of the incident time-harmonic electromagnetic plane wave and the electric far-field pattern of the scattered wave. A justification is given of the linear sampling method in this case and numerical examples are provided showing the practicality of our method.

scholarly journals An Inverse Mixed Impedance Scattering Problem in a Chiral Medium

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 104
Author(s):  
Evagelia S. Athanasiadou
Keyword(s):  
Electromagnetic Waves ◽  
A Priori ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Perfect Conductor ◽  
Impedance Boundary ◽  
Time Harmonic ◽  
Buried Object ◽  
Homogeneous Background

An inverse scattering problem of time-harmonic chiral electromagnetic waves for a buried partially coated object was studied. The buried object was embedded in a piecewise isotropic homogeneous background chiral material. On the boundary of the scattering object, the total electromagnetic field satisfied perfect conductor and impedance boundary conditions. A modified linear sampling method, which originated from the chiral reciprocity gap functional, was employed for reconstruction of the shape of the buried object without requiring any a priori knowledge of the material properties of the scattering object. Furthermore, a characterization of the impedance of the object’s surface was determined.

Far field patterns and the inverse scattering problem for electromagnetic waves in an inhomogeneous medium

1988 ◽  
Vol 103 (3) ◽  
pp. 561-575 ◽  
Author(s):  
David Colton ◽  
Lassi Päivärinta
Keyword(s):  
Inhomogeneous Medium ◽  
Inverse Scattering ◽  
Integral Identity ◽  
Electromagnetic Waves ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Optimal Solution ◽  
Far Field ◽  
Field Patterns

AbstractWe consider the scattering of time harmonic electromagnetic waves by an inhomogeneous medium of compact support. It is first shown that the set of far field patterns of the electric fields corresponding to incident plane waves propagating in arbitrary directions is complete in the space of square-integrable tangential vector fields defined on the unit sphere. We then show that under certain conditions the electric far field patterns satisfy an integral identity involving the unique solution of a new class of boundary value problems for Maxwell's equations called the interior transmission problem for electromagnetic waves. Finally, it is indicated how this integral identity can be used to formulate an optimization scheme yielding an optimal solution of the inverse scattering problem for electromagnetic waves.

Time harmonic electromagnetic waves in an inhomogeneous medium

1990 ◽  
Vol 116 (3-4) ◽  
pp. 279-293 ◽  
Author(s):  
David Colton ◽  
Rainer Kress
Keyword(s):  
Inhomogeneous Medium ◽  
Electromagnetic Waves ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Impedance Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Direct Scattering ◽  
Time Harmonic ◽  
Regularity Results

SynopsisWe consider the scattering of time harmonic electromagnetic waves by an inhomogeneous medium of compact support, i.e. the permittivity ε = ε(x) and the conductivity σ = σ(x) are functions of x ∊ ℝ3. Existence, uniqueness and regularity results are established for the direct scattering problem. Then, based on existence and uniqueness results for the exterior and interior impedance boundary value problem, a method is presented for solving the inverse scattering problem.

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