Workshop
on_
Inverse Obstacle Problems Program

More information on the location and hotels on this link 
November, 4
08h40
 Registration desk  until 11h00
09h0009h15  Wellcome
 Opening Session by
the President of Instituto Superior Técnico
09h2010h00  W.
Rundell  Inverse obstacles
problems in both the time and frequency domains
10h0010h40  R.
Potthast  The no response test 
a new sampling method for the reconstruction of bodies from scattered waves
10h4011h00  Coffee
Break
11h0011h40  A.
Ben Abda  Calderon type
fields and planar cracks recovery
11h4012h10  J.
Leblond  Pointwise sources recovery
and boundary approximations in 2D situations
12h1014h00  Lunch
time
14h0014h40  T.
Ha Duong  Identifying a
cavity by means of boundary measurements for the reduced wave equation
14h4015h10  A.
L. Silvestre  Identifying pointforces
on a Stokes system
15h1015h40  R.
Luke  On multifrequency extensions of
the point source method for inverse obstacle problems and ...
15h4016h00  Coffee
Break
16h0016h40  A.
El Badia  An inverse wave sources
problem
16h4017h10  T.
Hohage  Adaptive discretization of
the direct scattering problem in a regularized Newton method for the inverse
problem
17h2018h00  Poster Session
R. Casanova  Magnetic Inductance Tomography Imaging using Tikhonov regularization
M. Cristofol & P. Gaitan  Definition of the Scattering Amplitude for the Schrodinger Operator in a Layer
E. Francini  Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities
K. Y. Kim  Dynamic Electrical Impedance Tomography Based on the Extended Kalman Filter
M. C. Kim  Estimation of phase boundaries in electrical impedance tomography by adaptive mesh regeneration technique
S. Kim  Inverse Determination of Thermal Conductivity in a NonLinear Heat Conduction Medium
W. Pan  An Indicator Sampling Method for Solving Inverse Electromagnetic Obstacle Scattering from Near Field Measurements
P. Serranho  Identifying the flatness of a crack with acoustic scattering
V. Tsiporin  The Factorization Method for an Inverse Stokes Problem
November, 5
09h0009h40  R. Kress  Electrostatic
Imaging via Conformal Mapping
09h4010h20  H. Ammari  Reconstruction
of conductivity inhomogeneities
10h2010h40  Coffee Break
10h4011h20  F. Speck  An
operator theoretical concept for mixed linear boundary value problems
11h2012h00  F. Hettlich  Regularized
Newtontype methods for the recovery of periodic scattering objects
12h0014h00  Lunch time
14h0014h40  M. Jaoua  Numerical
algorithms for the solution of an inverse Robin problem
14h4015h20  I. Akduman  Inverse
Scattering Problems for Scatterers with Inhomogeneous Impedance Boundaries
15h2015h40  Coffee Break
15h4016h20  H. Orlande  Simultaneous
estimation of spatiallydependent diffusion coefficient and source term
in a nonlinear diffusion problem
16h2017h00  S. M. Jesus  Modelbased
inverse problems in underwater acoustics
20h00  Workshop dinner  Hotel Mundial (*) (25 Euros)
November, 6
09h0009h40  A. Kirsch  The
Factorization Method for a Class of Inverse Elliptic Problems
09h4010h10  T. Arens  The
Factorization Method in Scattering by Periodic Surfaces
10h1010h30  Coffee Break
10h3011h10  D. Lesnic  Inversion
of anisotropic conductivities
11h1011h50  L. Päivärinta
 Inverse scattering from a random
potential in 2D
11h5012h00  Closing Session
14h00  Bus Tour  Belém, Cascais, Cabo da Roca and Sintra. (*) (15 Euros)
Abstracts of the talks
H. Ammari (E. Polytechnique, France)
Reconstruction of conductivity inhomogeneities
Abstract:
We present a realtime algorithm for finding the location of a conductivity anomaly with a high resolution
as well as capturing details of the geometry of its interface.
The method is based on the derivation of an accurate asymptotic formula and the observation in both the near and
far field of the pattern of a simple weighted combination of the input currents and the output voltages.
( joint work with J. K. Seo )
I. Akduman (Istanbul Tech. Univ., Turkey)
Inverse Scattering Problems for Scatterers with Inhomogeneous Impedance Boundaries
Abstract:
Impedance Boundary Conditions (IBC) are the relations which connect the electric and magnetic field vectors
on a given surface in terms of a coefficient called surface impedance and the determination of the surface impedance
constitutes an important and interesting problem. The surface impedance of a given scatterer can be recovered through
the measured scattered data. Here, the cylindrical bodies of arbitrary shape having inhomogeneous surface impedances
are considered and a method to reconstruct the surface impedance from measured far field data is presented.
To this aim, the scattered field is first expressed in terms of a single layer potential which leads to an illposed
integral equation of the first kind for the density that requires stabilization for its numerical solution, for example by
Tikhonov regularization. With the aid of the jump relations, the singlelayer potential enables the evaluation of the total
field and its derivative on the boundary of the scatterer. Consequently, from the boundary condition finally the surface
impedance can be reconstructed either by direct evaluation or by a minimum norm solution in the least squares sense.
The numerical results show that our methods yields good resolution.
A. El Badia (Univ. Tech. Compiègne, France)
An inverse wave sources problem
Abstract:
This paper is concerned with an inverse point wave sources problem in a bounded domain W C R^{3}
from boundary observations. Assuming that all point sources vanish after a certain time T_{1}, we prove first an
identifiability result provided that some condition is satisfied between the time T_{1}, the observation interval (0, T)
and the observation domain on the boundary. This condition is reduced to the inequality T > T_{1} + diam(W)
when the observation domain is the whole boundary of W.
In this case, we propose a method to identify completely the sources: their number, locations and intensities.
( joint work with T. Ha Duong )
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F. Hettlich (Univ. Karlsruhe, Germany)
Regularized Newtontype methods for the recovery of periodic scattering objects
Abstract:
An inverse obstacle problem is investigated where the unknown object has a periodic structure.
We consider the scattering of an incident plane wave by such a periodic grating assuming Dirichlet boundary
conditions. A priori information on the hight of the scattering object ensures that the measurement of one
scattered field is sufficient in uniquely determine the structure. By deriving existence and a representation of
the first and second domain derivative of the scattered field it is shown that iterative regularization schemes
can be applied efficiently. The required solution of the forward boundary value problem is established
by an integral equation approach which utilizes the quasiperiodic fundamental solution. For the numerical
solution of the nonlinear severely illposed inverse problem, iterative regularization schemes are considered
based on the representation of the domain derivative. Additionally, the second derivative can be incorporated
by some advantage. The choice of regularization parameter and of an initial guess lead to well adapted regularization
schemes and numerical examples confirm the performance of such iterative approaches.
M. Jaoua (ENIT, Tunisia)
Numerical algorithms for the solution of an inverse Robin problem
Abstract:
The inverse problem of identifying a Robin coefficient on some part of the boundary of a smooth 2D domain,
from overdetermined data available on the other part of the boundary, is here considered for the Laplace equation.
This is the simplest model for corrosion detection by electric impedance tomography. After recalling results
regarding identifiability and stability, we address the identification issue by presenting two algorithms.
The first one is based on an energetic least square method, consisting in solving from the available data
(prescribed current flux and measured voltages), and a guess on the Robin coefficient, two boundary value problems,
a DirichletRobin and a NeumannRobin one, the cost function being their energy misfit. The method is proved to be
robust, and also selfregularizing. A gradient algorithm is worked out, providing satisfactory numerical results.
The second method consists in solving  from the precribed data  the Cauchy problem in order to recover the
whole data set on the Robin part of the boundary, using analytic extension tools. Such a problem is well known to
be severely illposed. To prevent the reconstructed solution from blowing up away from the prescription part of the
boundary, a bound is set on the data to be recovered, which leads to a so called bounded extremal problem.
The solution of such a problem may be explicitely computed as a series. However, doing so provides us with
nothing but an approximate extension, saturating the constraint, and is therefore arbitrary unless this constraint
happens to be the actual bound.
The algorithm thus needs to tackle both problems of determining the extension and the bound on its unknown part
in a single movement. To this end, the available prescribed data are split into two parts, each of them devoted to
fulfill one task, and a cross validation is performed. Another issue to consider is, since the purpose is to recover a
Robin coefficient from the extended data, that accuracy is not only needed on the function itself, but on its normal
derivative as well. This compels us to work out higher order methods, based on the same extension process.
The sobuilt identification scheme holds good convergence and accuracy properties, as well as robustness,
which is proved both theoretically and numerically.
( joint work with S. Chaabane, C. El Hechmi, J. Leblond )
S. M. Jesus (Univ. Algarve, Portugal)
Modelbased inverse problems in underwater acoustics
Abstract:
Possibly the most important development in underwater acoustics in the last century was the
introduction of modelbased processing (MBP). MBP is a junction between theory, under the form
of a computational solution of the wave equation with real world constraints, and practice, represented
by the field data. MBP was conjectured during the 70’s by M. Hinich and H. P. Bucker and attempted
with real data during the 80’s by several authors [Shang, Yang, Smith, Wilson, Heitmeyer, Jesus].
Nowadays, the impact of MBP can be seen in many fields like source detection and localization
(MFP), ocean acoustic tomography (OAT), matchedfield inversion for bottom properties (MFI) and
recently on underwater acoustic communications (UcomTRM).
One of the most interesting features provided by MBP is the possibility of attaining the inverse
solution by reversing the forward calculation. For most problems of practical interest (e.g. for sine waves),
the wave equation reduces to the Helmholtz equation which solution, depending on additional
assumptions, can be stated as a SturmLiouville problem by separation of variables, or as a set
of eikonal and transport equations by assuming a solution of the ray series type.
Unfortunately, analytical solutions are not known for realistic boundary conditions and sound
speed profiles.This paper briefly presents a collection of methods that have been used to solve
this inverse problem including, perturbation methods, neural network based and forward run
optimization either with direct or random algorithms. Examples with both simulated and real data
will be shown to illustrate the presented methods.
A. Kirsch (Univ. Karlsruhe, Germany)
The Factorization Method for a Class of Inverse Elliptic Problems
Abstract:
( extended abstract: psfile )
R. Kress (Univ. Göttingen, Germany)
Electrostatic Imaging via Conformal Mapping
Abstract:
We present the solution of an inverse boundary value problem for harmonic functions
arising in electrostatic imaging through conformal mapping techniques.
In a first step, by successive approximations a nonlinear equation is solved to determine the boundary
values of a holomorphic function on the outer boundary circle of an annulus.
Then in a second step an illposed Cauchy problem is solved to determine the holomorphic function in
the annulus and the unknown boundary is recovered as image of the inner boundary circle.
We establish convergence of the iteration procedure and through numerical examples we illustrate the
feasibility of the method.
D. Lesnic (Univ. Leeds, UK)
Inversion of anisotropic conductivities
Abstract:
An inverse problem is considered to identify the geometry of discontinuities in a conductive
material W C R^{d} with anisotropic conductivity I+(K  I)c_{D} from Cauchy data measurements taken on the
boundary of W, where D C W, K is a symmetric and positive definite tensor not equal to identity and c_{D} is
the characteristic function of the domain D.
As an example this models the determination of the shape, size and location of the anisotropic inner core
of the Earth from measurements taken at its mantle.
There are also other applications in electrical impedance tomography (EIT). The previous results of
Ikehata (1998) for estimating the size of the inclusion D are proved and applied to several examples.
Further, we develop an integral representation of the solution and we propose an efficient boundary element
method (BEM) in conjunction with a leastsquares constrained minimization procedure to detect an anisotropic
inclusion D, such as a circle, by a single boundary measurement. Numerical results are discussed confirming
the previous theoretical estimates of the size of the inclusion and giving an insight into the unresolved uniqueness
issues of detecting ellipses.
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H. Orlande (Univ. Fed. Rio Janeiro, Brazil)
Simultaneous estimation of spatiallydependent diffusion
coefficient and source term in a nonlinear diffusion problem
Abstract:
This work deals with the use of the conjugate gradient method with adjoint problem for the
simultaneous estimation of the spatially varying diffusion coefficient and of the spatially varying source
term, in a nonlinear diffusion problem. This work can be physically associated with the detection of
obstacles in heat conduction and in groundwater flow problems.
This inverse problem was solved by using a function estimation approach. Here, no information is a priori
assumed available regarding the functional forms of the unknown functions, except for the functional space
that they belong to. It is assumed that the unknowns belong to the Hilbert space of square integrable
functions in the spatial domain of interest.
The solution of inverse problems by using the conjugate gradient method with adjoint problem for function
estimation consists of the following basic steps:
(i) direct problem formulation, (ii) inverse problem formulation, (iii) sensitivity problems formulation,
(iv) adjoint problem formulation, (v) gradient equations, (vi) iterative solution procedure,
(vii) iteration process stopping criterion, and (viii) computational algorithm.
Such basic steps of the conjugate gradient method, as applied to the solution of the inverse problem under
consideration, are discussed in detail.
The accuracy of the present solution approach is examined by using simulated transient measurements
containing random errors in the inverse analysis. The effects of the number and locations of sensors, as
well as of the random measurement errors, on the inverse problem solution are examined. A typical nonlinear
heat conduction problem is taken as a testcase, in which the fluxes are specified on the boundaries and
temperature measurements can be taken in the medium. The inverse problems of independently estimating
either the diffusion coefficient or the source term (and assuming the other function as exactly known) are
also addressed.
( joint work with F. A. Rodrigues and G. S. Dulikravich)
L. Päivärinta (Univ. Oulu, Finland)
Inverse scattering from a random potential in 2D
Abstract:
In this talk we consider a scattering from a random potential in 2D.
We assume that the material is Markov. It follows that the potential is not a measure with probability one.
Thus we need to develop a scattering theory for potentials that are distributions ie. in Sobolev spaces with
negative smoothness. The main result is that the stochastic characteristics of the potential can be recovered
from one sample by using an averaged high frequency data.
( joint work with M. Lassas and E. Saksman )
R. Potthast (Univ. Göttingen, Germany)
The no response test  a new sampling method for the
reconstruction of bodies from scattered waves
Abstract:
We describe a novel scheme, which we call the 'no response test', to locate the support of a scatterer
from knowledge of a farfield pattern of a scattered acoustic wave. The method uses a set of sampling surfaces
and a special test response to detect the support of a scatterer without a priori knowledge of the physical properties
of the scatterer.
Specifically, the method does not depend on information about whether the scatterer is penetrable or impenetrable.
If the scatterer is penetrable, the nature of the inhomogeneity is not used. In contrast to previous sampling methods,
the methodology described here enables one to locate obstacles or inhomogeneities from the far field pattern of only
one or a few incident fields  the no response test is a onewavemethod.
We investigate the theoretical basis for the no response test and derive a new onewave uniqueness proof for a
region containing the scatterer. We show how to find the object within this region. We demonstrate the applicability
of the method by reconstructing soundsoft, soundhard, impedance and inhomogeneous medium scatterers in two
dimensions from one wave with full and limited aperture farfield pattern data.
F. Speck (IST, Portugal)
An operator theoretical concept for mixed linear boundary value problems
Abstract:
We consider a class of mixed boundary value problems in spaces of Bessel potentials.
By localization, an operator L associated with the BVP is related through operator matrix identities to a family
of pseudodifferential operators which leads to a Fredholm criterion for L .
But particular attention is devoted to the nonFredholm case where the image of L is not closed.
Minimal normalization, which means a certain minimal change of the spaces under consideration such that either
the continuous extension of L or the image restriction, respectively, is normally solvable, leads to modified spaces
of Bessel potentials. These can be characterized in a physically relevant sense and seen to be closely related to
operators with transmission property (domain normalization) or to problems with compatibility conditions for the
data (image normalization), respectively.
Tilo Arens(Univ.
Karlsruhe, Germany)
The Factorization
Method in Scattering by Periodic Surfaces
Abstract: The Factorization
Method of Kirsch has fast become a wellestablished method for the reconstruction
of bounded obstacles in inverse scattering problems. The method has also
been applied successfully to other classes of inverse problems such as
the reconstruction of cracks ins solids using impedance tomography.
It is the purpose of this
talk to explore the application of the Factorization Method to the inverse
problem of reconstructing a periodic surface. A major difference to bounded
obstacle scattering is that the far field data is known to not be sufficient
to reconstruct the surface uniquely. Various possible formulations of the
problem will be given and the applicability of the method demonstrated.
Numerical examples will illustrate the performance of the factorization
method for reconstructing periodic surfaces in practice.
Thorsten Hohage(Univ.
Goettingen, Germany)
Adaptive discretization
of the direct scattering problem in a
regularized Newton
method for the inverse problem
Abstract: We consider
the efficient numerical realization of the iteratively regularized GaussNewton
method for inverse obstacle problems using adaptive discretization of the
direct scattering problem. If the reconstruction is far away from the true
obstacle, it is not worth spending much computation time in solving the
direct problem accurately. Our aim is to improve the accuracy of the direct
problem solver in an optimal way as the reconstruction approaches the true
solution in the Newton iteration. The speed of convergence of the regularized
Newton method is governed by the smoothness of the true obstacle expressed
in terms of logarithmic source conditions. The key point of the convergence
analysis is to estimate the influence of operator perturbations on logarithmic
source conditions. The efficiency of the proposed scheme is illustrated
by numerical experiments with single and multiple obstacles.
Juliette Leblond(INRIA,
France)
Pointwise sources
recovery and boundary approximations in 2D situations
Abstract:
We approach the inverse
problem of determining pointwise conductivity defaults contained in an
interior layer from external boundary data.
In 2D cases, we show that
this issue can be expressed as a rational or meromorphic approximation
problem with constrained poles.
(
joint work with L. Baratchart & A. Ben Abda & F. Ben Hassen
)
D. Russell Luke(Univ.
Goettingen, Germany)
On multifrequency
extensions of the point source method for inverse
obstacle problems
and relations to classical filtered backprojection
Abstract: This
work outlines the point source method proposed by Potthast for solving
inverse scattering problems with single frequency data in the resonance
region and its connection to classical techniques for high frequency inverse
scattering problems. The connection suggests natural extensions of
the point source method, essentially a singlelowfrequency method, to
multifrequency settings. Elementary series expansions can be exploited
for efficient multifrequency implementation. We illustrate these techniques
with numerical examples.
A. L. Silvestre(Instituto
Superior Técnico, Portugal)
Identifying pointforces
on a Stokes system
Abstract: In
this work we address the problem of retrieving the location and intensities
of point forces associated with the motion of an incompressible viscous
fluid in steady slow regime. We apply a reciprocity gap function to obtain
a problem defined in the exterior of the fluid domain and retrieve the
location of these point forces in a nonlinear minimization problem.
(
joint work with C. J. S. Alves )
Ramón Casanova
Luis (IEETA
 Universidade de Aveiro, Portugal)
Magnetic Inductance
Tomography Imaging using Tikhonov regularization.
Abstract: Magnetic
Induction Tomography (MIT) is an imaging technique with potential applications
in medicine and industry. It is directed to image spatial distributions
of electrical conductivity and magnetic permeability of objects. Opposite
to other electrical imaging techniques, like ERT or ECT, MIT does not require
direct contact of the sensors (or electrodes) with the imaged object.
Image reconstruction is
related to the solution of a nonlinear inverse problem. In this work,
an algorithm based on Tikhonov regularization to image magnetic permeability
distribution of nonconducting ferromagnetic objects is presented. Assuming
spatial isotropy and linearity and the quasistatic approximation to the
Maxwell equations, the direct problem is modelled by the Laplace equation.
The inverse problem is linearized
through the use of a sensitivity matrix, obtained by estimating the system
response to a ferromagnetic cylinder, of a given diameter and magnetic
permeability, placed in welldefined positions within the imaging area.
The 9point 2D Laplacian is used as the regularization operator. The optimisation
of the Tikhonov functional is performed imposing to the solution a nonnegativity
constraint.
Results are compared with
those obtained by minimumnorm inversion and Tikhonov regularization without
a constraint. It is shown that a good localization of the objects is achieved
even when a strong gaussian uncorrelated noise is added to the projection
data.
(
joint work with
A. Ferreira da Silva & A. Rui Borges
)
Michel Cristofol
(CMI,
Université de Provence, France)
Patricia Gaitan
(CMI,
Université de Provence, France)
Definition of
the Scattering Amplitude for the Schrodinger Operator in a Layer.
Abstract: There is
no definition for the scattering amplitude for the Schrödinger operator
in a threedimensional layer. The aim of this work is, in a first step
to correctly define this scattering amplitude and in a second step to give
an uniqueness theorem for the inverse potential problem.
Elisa Francini
(Istituto
per le Applicazioni del Calcolo, Italy)
Asymptotic formulas
for steady state voltage potentials in the presence of thin inhomogeneities
Abstract: Consider
an electrically conducting medium with thin conductivity inhomogeneities.
We provide a rigorous derivation
of the leading terms in an asymptotic expansion of the steady state boundary
voltage potentials,
as the thickness of the
inhomogeneities goes to zero.
(
joint work with E. Beretta and M. Vogelius
)
Kyung Youn Kim
(Cheju
National University, S. Korea)
Dynamic Electrical
Impedance Tomography
Based on the
Extended Kalman Filter
Abstract: Image
reconstruction in EIT is a nonlinear inverse problem in which the resistivity
distribution inside of the object is estimated based on the knowledge of
the injected currents and measured voltages on the boundary of the object.
Most of the reconstruction algorithms developed so far are mainly focused
on the static cases where the internal resistivity of the object is timeinvariant
within the time taken to acquire a full set of measurement data. In this
paper, an effective dynamic EIT imaging scheme is presented based on the
extended Kalman filter for the case where the resistivity distribution
inside the object changes rapidly in time. The inverse problem is treated
as nonlinear state estimation problem by employing the hypermodel as state
evolution model. By taking into account the first or secondorder derivative
in the target motion analysis, the modeling uncertainty is reduced significantly.
In particular, preintegration technique is also introduced to stabilize
the inverse solver. By preintegration we mean that some part of the elements
are grouped together before the reconstruction to reduce the states to
be estimated. The reconstruction performance in terms of the spatial and
temporal resolution is enhanced considerably compared to that of the conventional
techniques.
(
joint work with S.I. Kang & B.S. Kim & M.C. Kim & S.
Kim )
Min Chan Kim (Cheju
National University, S. Korea)
Estimation of
phase boundaries in electrical impedance tomography
by adaptive mesh
regeneration technique
Abstract: Twophase
flow can occur under the normal and accidental conditions in various processes
such as heat exchanger, steam power generation and oil or natural gas pumping
system. Because the phase distribution affects the safety, control, operation
and optimization of process, it is important to know the phase boundaries
in online without disturbing the flow field. Recently, the electrical
tomography technique is employed to investigate twophase flow phenomena,
because it is relatively inexpensive and has good time resolution. In the
present study, an new image reconstruction algorithm employing adaptive
mesh regeneration technique was developed for the detection of phase boundaries.
The phase boundaries were expressed as truncated Fourier series and the
Fourier coefficients were estimated with the aid of finite element calculation.
To test the feasibility of the method, some numerical simulations were
conducted.
(
joint work with Kyung Yeon Kim & Sin Kim & Yoon
Joon Lee )
Sin Kim (Cheju
National University, S. Korea)
Inverse Determination
of Thermal Conductivity
in a NonLinear
Heat Conduction Medium
Abstract: An
integral method is proposed to estimate temperaturedependent thermal conductivity
with no interior measurements in a onedimensional heat conduction medium.
We consider the thermal conductivity of an arbitrary functional form, which
can be approximated as a piecewise linear function. Each piece of linear
function within the temperature range of interest has two unknown coefficients
and they will be estimated from the balance equation derived from the integral
heat conduction equation. To solve the balance equation, that is to estimate
the unknown coefficients, the temperature distribution should be known
a priori, however it could not be available. In the present work, the temperature
distribution is approximated as a thirdorder polynomial that satisfies
the overspecified boundary conditions. Their coefficients will be timedependent
and can be expressed in terms of the imposed boundary heat fluxes, the
measured boundary temperatures, and the unknown coefficients. With this
approximated temperature profile, each set of unknown coefficients identifying
the corresponding piecewise linear thermal conductivity is determined and
assembling each linear function we can estimate the thermal conductivity
of an arbitrary function. It should be noted that the procedure doesn't
require solving the heat conduction equation. Some examples are introduced
to examine the performance of the proposed algorithm.
(
joint work with
Min Chan Kim & Kyung Youn Kim & Bum Jin Chung
& Junghoon Lee)
Wenfeng Pan (Wuhan
University of Technology, China)
An Indicator
Sampling Method for Solving Inverse Electromagnetic
Obstacle Scattering
from Near Field Measurements
Abstract: We derive
the formulation corresponding to inverse obstacle and generalize the conclusion
on acoustic wave corresponding to field to more general case on electromagnetic
wave for indicator sampling method,which is not the same as general iteration
method either with plane wave or spherical wave incident. It doesn't need
to solve direct problem,less about it's computational time consume and
only requires knowledge of general location of the unknown scatterer. Finally,as
the experiment,we obtain the image of obstacle in structure and material
successfully.
Pedro Serranho
(Instituto
Superior Técnico, Portugal)
Identifying the
flatness of a crack by acoustic scattering
Abstract: We present
simulations of the far field pattern generated by nonflat acoustic cracks
in 3D, using the variational formulation of the boundary integral equation
to avoid the hypersingularity in the double layer potential.
These simulations show the
direct relation between a far field plane having almost null amplitude
and the main directions of a plane that defines a quasiflat crack.
(
joint work with
C.J.S. Alves )
Viktor Tsiporin
(University
of Goettingen, Germany)
The Factorization
Method for an Inverse Stokes Problem
Abstract: We consider
an inverse boundary value problem associated with the twodimensional Stokes
equation and Dirichlet boundary condition.
This problem requires the
reconstruction of the shape of an unknown object from measurements of the
responding velocity fields with sources and receivers placed along a curve
surrounding the object. Our approach is based on the Kirsch factorization
method, whose main advantage is that no a priori assumptions about the
shape of the object are needed. We give a theoretical foundation for the
feasibility of this method and validate it by numerical experiments.