241 research outputs found
3D direct and inverse solvers for eddy current testing of deposits in steam generator
We consider the inverse problem of estimating the shape profile of an unknown
deposit from a set of eddy current impedance measurements. The measurements are
acquired with an axial probe, which is modeled by a set of coils that generate
a magnetic field inside the tube. For the direct problem, we validate the
method that takes into account the tube support plates, highly conductive part,
by a surface impedance condition. For the inverse problem, finite element and
shape sensitivity analysis related to the eddy current problem are provided in
order to determine the explicit formula of the gradient of a least square
misfit functional. A geometrical-parametric shape inversion algorithm based on
cylindrical coordinates is designed to improve the robustness and the quality
of the reconstruction. Several numerical results are given in the experimental
part. Numerical experiments on synthetic deposits, nearby or far away from the
tube, with different shapes are considered in the axisymmetric configuration.Comment: 3
On the asymptotics of a Robin eigenvalue problem
The considered Robin problem can formally be seen as a small perturbation of
a Dirichlet problem. However, due to the sign of the impedance value, its
associated eigenvalues converge point-wise to as the perturbation
goes to zero. We prove that in this case, Dirichlet eigenpairs are the only
accumulation points of the Robin eigenpairs with normalized eigenvectors. We
then provide a criteria to select accumulating sequences of eigenvalues and
eigenvectors and exhibit their full asymptotic with respect to the small
parameter
Generalized linear sampling method for elastic-wave sensing of heterogeneous fractures
A theoretical foundation is developed for active seismic reconstruction of
fractures endowed with spatially-varying interfacial condition
(e.g.~partially-closed fractures, hydraulic fractures). The proposed indicator
functional carries a superior localization property with no significant
sensitivity to the fracture's contact condition, measurement errors, and
illumination frequency. This is accomplished through the paradigm of the
-factorization technique and the recently developed Generalized
Linear Sampling Method (GLSM) applied to elastodynamics. The direct scattering
problem is formulated in the frequency domain where the fracture surface is
illuminated by a set of incident plane waves, while monitoring the induced
scattered field in the form of (elastic) far-field patterns. The analysis of
the well-posedness of the forward problem leads to an admissibility condition
on the fracture's (linearized) contact parameters. This in turn contributes
toward establishing the applicability of the -factorization method,
and consequently aids the formulation of a convex GLSM cost functional whose
minimizer can be computed without iterations. Such minimizer is then used to
construct a robust fracture indicator function, whose performance is
illustrated through a set of numerical experiments. For completeness, the
results of the GLSM reconstruction are compared to those obtained by the
classical linear sampling method (LSM)
A generalized formulation of the Linear Sampling Method with exact characterization of targets in terms of farfield measurements
International audienceWe propose and analyze a new formulation of the Linear Sampling Method that uses an exact characterization of the targets shape in terms of the so-called farfield operator (at a fixed frequency). This characterization is based on constructing nearby solutions of the farfield equation using minimizing sequences of a least squares cost functional with an appropriate penalty term. We first provide a general framework for the theoretical foundation of the method in the case of noise-free and noisy measurements operator. We then explicit applications for the case of inhomogeneous inclusions and indicate possible straightforward generalizations. We finally validate the method through some numerical tests and compare the performances with classical LSM and the factorization methods
Asymptotic models for scattering problems from unbounded media with high conductivity
We analyze the accuracy and well-posedness of generalized impedance boundary value problems in the framework of scattering problems from unbounded highly absorbing media. We restrict ourselves in this first work to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties in the analysis for the generalized impedance boundary conditions, since classical compactness arguments are no longer possible. Our new analysis is based on the use of Rellich-type estimates and boundedness of solution operators. We also discuss numerical approximation of obtained GIBC (up to order 3) and numerically test theoretical convergence rates
Numerical analysis of the factorization method for EIT with a piecewise constant uncertain background
International audienceWe extend the factorization method for electrical impedance tomography to the case of background featuring uncertainty. We first describe the algorithm for the known but inhomogeneous backgrounds and indicate expected accuracy from the inversion method through some numerical tests. Then we develop three methodologies to apply the factorization method to the more difficult case of a piecewise constant but uncertain background. The first one is based on a recovery of the background through an optimization scheme and is well adapted to relatively low-dimensional random variables describing the background. The second one is based on a weighted combination of the indicator functions provided by the factorization method for different realizations of the random variables describing the uncertain background. We show through numerical experiments that this procedure is well suited to the case where many realizations of the measurement operators are available. The third strategy is a variant of the previous one when measurements for the inclusion-free background are available. In this case, a single pair of measurements is sufficient to achieve comparable accuracy to the deterministic case
Numerical analysis of the Factorization Method for Electrical Impedance Tomography in inhomogeneous medium
The retrieval of information on the coefficient in Electrical Impedance Tomography is a severely ill-posed problem, and often leads to inaccurate solutions. It is well known that numerical methods provide only low-resolution reconstructions. The aim of this work is to analyze the Factorization Method in the case of inhomogeneous background. We propose a numerical scheme to solve the dipole-like Neumann boundary-value problem, when the background coefficient is inhomogeneous. Several numerical tests show that the method is capable of recovering the location and the shape of the inclusions, in many cases where the diffusion coefficient is nonlinearly space-dependent. In addition, we test the numerical scheme after adding artificial noise
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