Workshop on_
 Inverse
Obstacle
Problems


 

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November, 4

08h40 - Registration desk - until 11h00
09h00-09h15 - Wellcome - Opening Session by the President of Instituto Superior Técnico
09h20-10h00 - W. Rundell - Inverse obstacles problems in both the time and frequency domains
10h00-10h40 - R. Potthast - The no response test - a new sampling method for the reconstruction of bodies from scattered waves
10h40-11h00 - Coffee Break
11h00-11h40 - A. Ben Abda - Calderon type fields and planar cracks recovery
11h40-12h10 - J. Leblond - Pointwise sources recovery and boundary approximations in 2D situations
12h10-14h00 - Lunch time
14h00-14h40 - T. Ha Duong - Identifying a cavity by means of boundary measurements for the reduced wave equation
14h40-15h10 - A. L. Silvestre - Identifying point-forces on a Stokes system
15h10-15h40 - R. Luke - On multifrequency extensions of the point source method for inverse obstacle problems and ...
15h40-16h00 - Coffee Break
16h00-16h40 - A. El Badia - An inverse wave sources problem
16h40-17h10 - T. Hohage - Adaptive discretization of the direct scattering problem in a regularized Newton method for the inverse problem

17h20-18h00 - 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 Non-Linear 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

09h00-09h40 - R. Kress - Electrostatic Imaging via Conformal Mapping
09h40-10h20 - H. Ammari - Reconstruction of conductivity inhomogeneities
10h20-10h40 - Coffee Break
10h40-11h20 - F. Speck - An operator theoretical concept for mixed linear boundary value problems
11h20-12h00 - F. Hettlich - Regularized Newton-type methods for the recovery of periodic scattering objects
12h00-14h00 - Lunch time
14h00-14h40 - M. Jaoua - Numerical algorithms for the solution of an inverse Robin problem
14h40-15h20 - I. Akduman - Inverse Scattering Problems for Scatterers with Inhomogeneous Impedance Boundaries
15h20-15h40 - Coffee Break
15h40-16h20 - H. Orlande - Simultaneous estimation of spatially-dependent diffusion coefficient and source term in a nonlinear diffusion problem
16h20-17h00 - S. M. Jesus - Model-based inverse problems in underwater acoustics

20h00 - Workshop dinner - Hotel Mundial (*) (25 Euros)


November, 6

09h00-09h40 - A. Kirsch - The Factorization Method for a Class of Inverse Elliptic Problems
09h40-10h10 - T. Arens - The Factorization Method in Scattering by Periodic Surfaces
10h10-10h30 - Coffee Break
10h30-11h10 - D. Lesnic - Inversion of anisotropic conductivities
11h10-11h50 - L. Päivärinta - Inverse scattering from a random potential in 2D
11h50-12h00 - Closing Session

14h00 - Bus Tour - Belém, Cascais, Cabo da Roca and Sintra. (*) (15 Euros)



(*) In order to make your reservation, please pay in advance at the registration desk, monday morning until 11h00.


 
 






















Abstracts of the talks



 
 






H. Ammari (E. Polytechnique, France)
Reconstruction of conductivity inhomogeneities
Abstract:
We present a real-time 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 ill-posed
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 single-layer 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 R3
from boundary observations.  Assuming that all point sources vanish after a certain time T1, we prove first an
identifiability result provided that some condition is satisfied between the time T1, the observation interval (0, T)
and the observation domain on the boundary.  This condition is reduced to the inequality T > T1 + 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 Newton-type 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 quasi-periodic fundamental solution. For the numerical
solution of the nonlinear severely  ill-posed 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 Dirichlet-Robin and a Neumann-Robin one, the cost function being their energy misfit. The method is proved to be
robust, and also self-regularizing. 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 ill-posed. 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 so-built 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)
Model-based inverse problems in underwater acoustics
Abstract:
Possibly the most important development in underwater acoustics in the last century was the
introduction of model-based 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 70ís by M. Hinich and H. P. Bucker and attempted
with real data during the 80ís 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), matched-field inversion for bottom properties (MFI) and
recently on underwater acoustic communications (Ucom-TRM).
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 Sturm-Liouville 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: ps-file )
 
 




















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 ill-posed 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 Rd with anisotropic conductivity I+(K - I)cD 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 cD 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 least-squares 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 spatially-dependent 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 test-case, 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 far-field 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 one-wave-method.
We investigate the theoretical basis for the no response test and derive a new one-wave 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 sound-soft, sound-hard, impedance and inhomogeneous medium scatterers in two
dimensions from one wave with full and limited aperture far-field 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 pseudo-differential operators which leads to a Fredholm criterion for L .
But particular attention is devoted to the non-Fredholm 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 well-established 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 Gauss-Newton 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 multi-frequency 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 single-low-frequency method, to  multi-frequency settings. Elementary series expansions can be exploited for efficient multi-frequency implementation. We illustrate these techniques with numerical examples.
 
 
 
 
 
 
 
 
 


A. L. Silvestre(Instituto Superior Técnico, Portugal)
Identifying point-forces 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 )
 
 
 
 
 
 
 
 
 



 
 




















Poster Session


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 non-linear inverse problem. In this work, an algorithm based on Tikhonov regularization to image magnetic permeability distribution of non-conducting ferromagnetic objects is presented. Assuming spatial isotropy and linearity and the quasi-static 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 well-defined positions within the imaging area. The 9-point 2D Laplacian is used as the regularization operator. The optimisation of the Tikhonov functional is performed imposing to the solution a non-negativity constraint.
Results are compared with those obtained by minimum-norm 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 three-dimensional 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 time-invariant 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 hyper-model as state evolution model. By taking into account the first- or second-order derivative in the target motion analysis, the modeling uncertainty is reduced significantly. In particular, pre-integration technique is also introduced to stabilize the inverse solver. By pre-integration 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:  Two-phase 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 on-line without disturbing the flow field. Recently, the electrical tomography technique is employed to investigate two-phase 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 Non-Linear Heat Conduction Medium
Abstract:  An integral method is proposed to estimate temperature-dependent thermal conductivity with no interior measurements in a one-dimensional 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 third-order polynomial that satisfies the over-specified boundary conditions. Their coefficients will be time-dependent 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 non-flat 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 quasi-flat 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 two-dimensional 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.