scholarly journals Identification of an unbounded bi-periodic interface for the inverse fluid-solid interaction problem

2021 ◽  
Author(s):  
Yanli Cui ◽  
Fenglong Qu ◽  
Changkun Wei
Keyword(s):  
Acoustic Waves ◽  
Near Field ◽  
A Priori ◽  
Scattering Problem ◽  
Three Dimensional ◽  
A Priori Estimate ◽  
Countably Infinite ◽  
Fluid Solid Interaction ◽  
Interaction Problem ◽  
Scattering Of Acoustic Waves

This paper is concerned with the inverse scattering of acoustic waves by an unbounded periodic elastic medium in the three-dimensional case. A novel uniqueness theorem is proved for the inverse problem of recovering a bi-periodic interface between acoustic and elastic waves using the near-field data measured only from the acoustic side of the interface, corresponding to a countably infinite number of quasi-periodic incident acoustic waves. The proposed method depends only on a fundamental a priori estimate established for the acoustic and elastic wave fields and a new mixed-reciprocity relation established in this paper for the solutions of the fluid-solid interaction scattering problem.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

Dielectric Metrology VIA Microwave Tomography: Present and Future

1994 ◽  
Vol 347 ◽  
Author(s):  
J.Ch. Bolomey ◽  
N. Joachimowicz
Keyword(s):  
Inverse Scattering ◽  
A Priori ◽  
Scattering Problem ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Dielectric Characterization ◽  
Sample Shape ◽  
Three Dimensional Configuration ◽  
Characterization Of Materials

ABSTRACTUntil now, the measurement techniques used for the dielectric characterization of materials require severe limitations in terms of sample shape, size and homogeneity. This paper considers the dielectric permittivity measurement as a non-linear inverse scattering problem. Such an approach allows to identify the quantities to be measured and suggests possible experimental arrangements. The problem is shown to be significantly simplified if the shape of the material is known and if some a priori knowledge of the averaged value of the permittivity in the material under test is available. Two test cases have been selected to illustrate the state of the art in solving such inverse problems. The first one consists of a two-dimensional configuration which is applicable to cylindrical objects, and the second one to a vector three-dimensional configuration applicable, for instance, to cubic samples. The main limitations of such an inverse scattering approach are discussed and expected improvements in the near future are analysed.

scholarly journals 3D Imaging of Buried Dielectric Targets with a Tomographic Microwave Approach Applied to GPR Synthetic Data

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Alessandro Galli ◽  
Davide Comite ◽  
Ilaria Catapano ◽  
Gianluca Gennarelli ◽  
Francesco Soldovieri ◽  
...  
Keyword(s):  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Numerical Data ◽  
Shallow Subsurface ◽  
Different Shapes ◽  
3D Information ◽  
Ground Penetrating

Effective diagnostics with ground penetrating radar (GPR) is strongly dependent on the amount and quality of available data as well as on the efficiency of the adopted imaging procedure. In this frame, the aim of the present work is to investigate the capability of a typical GPR system placed at a ground interface to derive three-dimensional (3D) information on the features of buried dielectric targets (location, dimension, and shape). The scatterers can have size comparable to the resolution limits and can be placed in the shallow subsurface in the antenna near field. Referring to canonical multimonostatic configurations, the forward scattering problem is analyzed first, obtaining a variety of synthetic GPR traces and radargrams by means of a customized implementation of an electromagnetic CAD tool. By employing these numerical data, a full 3D frequency-domain microwave tomographic approach, specifically designed for the inversion problem at hand, is applied to tackle the imaging process. The method is tested here by considering various scatterers, with different shapes and dielectric contrasts. The selected tomographic results illustrate the aptitude of the proposed approach to recover the fundamental features of the targets even with critical GPR settings.

A Sampling Method to an Inverse Scattering Problem for Stationary Schrödinger Equation

2013 ◽  
Vol 275-277 ◽  
pp. 1585-1589
Author(s):  
Yuan Li ◽  
Ming Chen Yao ◽  
Chun Mei Wang ◽  
Fa Yong Zhang
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Sampling Method ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Potential Scattering ◽  
Stationary Schrödinger Equation ◽  
Direct Sampling

For an inverse potential scattering problem of stationary Schrödinger equation, we employ a direct sampling method to reconstruct the support of the potential. Compared with the general sampling method, the method we adopt is applicable even when the measured data (near-field data) are only available for one or several incident directions, and has the advantages of simple computation and insensitivity to noises. By the mathematical derivations, we conclude theoretically that for both two dimensional and three dimensional cases, this direct sampling method is feasible and efficient.

scholarly journals The determination of the surface impedance of an obstacle

1993 ◽  
Vol 36 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Andrzej W. Kȩdzierawski
Keyword(s):  
Acoustic Waves ◽  
Surface Impedance ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Far Field ◽  
Field Patterns ◽  
Time Harmonic ◽  
Scattered Fields

The inverse scattering problem we consider is to determine the surface impedance of a three-dimensional obstacle of known shape from a knowledge of the far-field patterns of the scattered fields corresponding to many incident time-harmonic plane acoustic waves. We solve this problem by using both the methods of Kirsch-Kress and Colton-Monk.

Linear Sampling and Reciprocity Gap Methods for a Fluid–Solid Interaction Problem in the Near Field

2011 ◽  
Author(s):  
Peter Monk ◽  
Virginia Selgas ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Near Field ◽  
Fluid Solid Interaction ◽  
Interaction Problem ◽  
Linear Sampling

scholarly journals ANALYTIC PRECONDITIONERS FOR THE BOUNDARY INTEGRAL SOLUTION OF THE SCATTERING OF ACOUSTIC WAVES BY OPEN SURFACES

2005 ◽  
Vol 13 (03) ◽  
pp. 477-498 ◽  
Author(s):  
XAVIER ANTOINE ◽  
ABDERRAHMANE BENDALI ◽  
MARION DARBAS
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Solution ◽  
Open Surface ◽  
Efficient Tool ◽  
Closed Surfaces ◽  
Scattering Of Acoustic Waves

This study is devoted to some numerical issues in the boundary integral solution of the scattering of an acoustic wave by an open surface. More precisely, it deals with the construction of a cheap analytical preconditioner to enhance the iterative solving of this kind of equation. Detailed attention is paid to bring out the reasons that make this construction much more difficult than for closed surfaces. This preconditioner is carefully tested and compared to two more usual ones for two and three dimensional problems. It is shown that this preconditioner provides a cheap and efficient tool making reliable the iterative solving. The discussion also precisely brings out the issues where further studies are still needed to improve its efficiency.

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