scholarly journals Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Jun Guo ◽  
Guozheng Yan ◽  
Mingjian Cai
Keyword(s):  
Boundary Condition ◽  
Scattering Problem ◽  
Plane Waves ◽  
Homogeneous Medium ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Impedance Boundary Condition ◽  
Mathematical Basis ◽  
Impedance Boundary

This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the solution to the direct scattering problem is established by using the boundary integral method. Then a uniqueness result for the inverse scattering problem is proved; that is, both of the obstacle’s shape and the impedances (μ,λ) can be uniquely determined from far field measurements. Furthermore, a mathematical basis is given to reconstruct the shape of the obstacle by using a modified linear sampling method.

Far field patterns and inverse scattering problems for imperfectly conducting obstacles

1989 ◽  
Vol 106 (3) ◽  
pp. 553-569 ◽  
Author(s):  
T. S. Angell ◽  
David Colton ◽  
Rainer Kress
Keyword(s):  
Boundary Condition ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Impedance Boundary Condition ◽  
Far Field ◽  
Scattering Problems ◽  
Impedance Boundary ◽  
Field Patterns

AbstractWe first examine the class of far field patterns for the scalar Helmholtz equation in ℝ2 corresponding to incident time harmonic plane waves subject to an impedance boundary condition where the impedance is piecewise constant with respect to the incident direction and continuous with respect to x ε ∂ D where ∂ D is the scattering obstacle. We then examine the class of far field patterns for Maxwell's equations in subject to an impedance boundary condition with constant impedance. The results obtained are used to derive optimization algorithms for solving the inverse scattering problem.

scholarly journals The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yao Mao ◽  
Yongguang Chen ◽  
Jun Guo
Keyword(s):  
Boundary Condition ◽  
Inverse Scattering ◽  
Surface Impedance ◽  
Near Field ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Inverse Scattering Problem ◽  
Impedance Boundary Condition ◽  
Mathematical Basis ◽  
Impedance Boundary

We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.

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