Near field sampling type methods for the inverse fluid--solid interaction problem
Peter Monk,Virginia Selgas +1 more
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In this article, the inverse fluid-solid interaction problem is considered, where the elastic body is probed by pressure waves due to point sources, and the resulting scattered field and the normal derivative of the scattered field is available for every source and receiver combination on the source and measurement curves.Abstract:
The inverse fluid--solid interaction problem considered here is to determine the shape of an elastic body from pressure measurements made in the near field. In particular we assume that the elastic body is probed by pressure waves due to point sources, and the resulting scattered field and the normal derivative of the scattered field is available for every source and receiver combination on the source and measurement curves. We provide an analysis of the Reciprocity Gap (RG) method in this case, as well as the Linear Sampling Method (LSM). A novelty of our analysis is that we exhibit a connection between the RG method and a non--standard LSM using sources and receivers on different curves. We provide numerical tests of the algorithms using both synthetic and real data.read more
Citations
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Boundary Integral Equation Methods for the Two-Dimensional Fluid-Solid Interaction Problem
Tao Yin,George C. Hsiao,Liwei Xu +2 more
TL;DR: In this article, boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem have been studied and the existence and uniqueness results for variational solutions of boundary integral equations are established.
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Sampling type methods for an inverse waveguide problem
Peter Monk,Virginia Selgas +1 more
TL;DR: In this paper, the problem of locating a penetrable obstacle in an acoustic waveguide from measurements of pressure waves due to point sources inside the waveguide is considered. But the obstacle is allowed to touch the boundary of the pipe.
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The reciprocity gap functional method for the inverse scattering problem for cavities
Yao Sun,Yukun Guo,Fuming Ma +2 more
TL;DR: In this paper, the shape of a perfectly conducting cavity from the Cauchy data on a curve inside the cavity was determined by using the near-field linear sampling method (LSM) with mere the scattered field.
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The Factorization Method for an inverse fluid-solid interaction scattering problem
Andreas Kirsch,Albert Ruiz +1 more
TL;DR: In this article, the authors justify the Factorization Method for a coupled acoustic-elastic medium under natural assumptions on the data and prove an explicit form of the characteristic function of the scattering medium $D$ where only the spectral data of the far field operator enter.
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Recovering an elastic obstacle containing embedded objects by the acoustic far-field measurements
TL;DR: In this paper, the inverse scattering problem of time-harmonic acoustic waves by a 3D bounded elastic obstacle, which may contain embedded impenetrable obstacles inside, is considered and the elastic obstacle can be uniquely recovered by the acoustic far-field pattern at a fixed frequency, disregarding its contents.
References
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Book
Inverse Acoustic and Electromagnetic Scattering Theory
David Colton,Rainer Kress +1 more
TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).
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Recent Developments in Inverse Acoustic Scattering Theory
TL;DR: This presentation surveys some of the highlights of inverse scattering theory as it has developed over the last 15 years, with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves.
Journal ArticleDOI
A simple method using Morozov's discrepancy principle for solving inverse scattering problems
TL;DR: In this paper, a simple inversion scheme was given for inverse scattering problems in the resonance region which is easy to implement and is relatively independent of the geometry and physical properties of the scatterer.
Journal ArticleDOI
An application of the reciprocity gap functional to inverse scattering theory
David Colton,Houssem Haddar +1 more
TL;DR: In this article, a method for determining the shape of an object from the Cauchy data of the total field measured on the boundary of a domain containing the object in its interior is given.
Journal ArticleDOI
Fluid-solid interaction: acoustic scattering by a smooth elastic obstacle
C. J. Luke,Paul A. Martin +1 more
TL;DR: A bounded three-dimensional elastic obstacle is surrounded by an unbounded inviscid compressible fluid; acoustic waves are scattered by the obstacle; the problem is to find the scattered waves and the response of the obstacle.