An analysis of the accuracy of the linear sampling method for an acoustic inverse obstacle scattering problem

2009 ◽  
Vol 26 (1) ◽  
pp. 015010 ◽  
Author(s):  
Nguyen Trung Thành ◽  
Mourad Sini
Keyword(s):  
Sampling Method ◽  
Scattering Problem ◽  
Linear Sampling Method ◽  
Obstacle Scattering ◽  
Inverse Obstacle Scattering ◽  
Linear Sampling

scholarly journals DIRECT AND INVERSE ACOUSTIC SCATTERING BY A COMBINED SCATTERER

2015 ◽  
Vol 20 (3) ◽  
pp. 422-442
Author(s):  
Jing Jin ◽  
Jun Guo ◽  
Mingjian Cai
Keyword(s):  
Inhomogeneous Medium ◽  
Sampling Method ◽  
Scattering Problem ◽  
Plane Waves ◽  
Acoustic Scattering ◽  
Uniqueness Result ◽  
Field Pattern ◽  
Linear Sampling Method ◽  
Far Field Pattern ◽  
Linear Sampling

This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by a union of a crack and a penetrable inhomogeneous medium with compact support. The well-posedness of the direct problem is established by the variational method. An uniqueness result for the inverse problem is proved, that is, both the crack and the inhomogeneous medium can be uniquely determined by a knowledge of the far-field pattern for incident plane waves. The linear sampling method is employed to recover the location and shape of the combined scatterer. It is worth noting that we make the first step on reconstructing a mixed-type scatterer of a crack and an inhomogeneous medium by the linear sampling method.

scholarly journals Target signatures for thin surfaces

2021 ◽  
Author(s):  
Fioralba Cakoni ◽  
Peter B. Monk ◽  
Yangwen Zhang
Keyword(s):  
Sampling Method ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Data ◽  
Open Surface ◽  
Linear Sampling Method ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Theoretical Results ◽  
Linear Sampling

Abstract We investigate an inverse scattering problem for a thin inhomogeneous scatterer in ${\mathbb R}^m$, $m=2,3$, which we model as a $m-1$ dimensional open surface. The scatterer is referred to as a screen. The goal is to design target signatures that are computable from scattering data in order to detect changes in the material properties of the screen. This target signature is characterized by a mixed Steklov eigenvalue problem for a domain whose boundary contains the screen. We show that the corresponding eigenvalues can be determined from appropriately modified scattering data by using the generalized linear sampling method. A weaker justification is provided for the classical linear sampling method. Numerical experiments are presented to support our theoretical results.

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