@article{2015arXiv150206723H,
abstract = {This work is motivated by the monitoring of conductive clogging deposits in steam generator at the level of support plates. One would like to use monoaxial coils measurements to obtain estimates on the clogging volume. We propose a 3D shape optimization technique based on simplified parametrization of the geometry adapted to the measurement nature and resolution. The direct problem is modeled by the eddy current approximation of time-harmonic Maxwell's equations in the low frequency regime. A potential formulation is adopted in order to easily handle the complex topology of the industrial problem setting. We first characterize the shape derivatives of the deposit impedance signal using an adjoint field technique. For the inversion procedure, the direct and adjoint problems have to be solved for each coil vertical position which is excessively time and memory consuming. To overcome this difficulty, we propose and discuss a steepest descent method based on a fixed and invariant triangulation. Numerical experiments are presented to illustrate the convergence and the efficiency of the method.},
archivePrefix = {arXiv},
arxivId = {math.NA/1502.06723},
author = {Haddar, Houssem and Riahi, M.{\~{}}K. Mohamed Kamel and Jiang, Zixian and Riahi, M.{\~{}}K. Mohamed Kamel},
doi = {http://arxiv.org/pdf/1502.06723.pdf},
eprint = {1502.06723},
isbn = {1091501602},
issn = {08857474},
journal = {Journal of Scientific Computing},
keywords = {Electromagnetism,Inverse problem,Mathematics - Analysis of PDEs,Mathematics - Numerical Analysis,Mathematics - Optimization and Control,Non-destructive testing,Shape optimization,Time-harmonic eddy current},
month = {feb},
number = {1},
pages = {29--59 (30)},
primaryClass = {math.NA},
title = {{A robust inversion method for quantitative 3D shape reconstruction from coaxial eddy-current measurements}},
url = {http://arxiv.org/pdf/1502.06723.pdf},
volume = {70},
year = {2017}
}

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We first characterize the shape derivatives of the deposit impedance signal using an adjoint field technique. For the inversion procedure, the direct and adjoint problems have to be solved for each coil vertical position which is excessively time and memory consuming. To overcome this difficulty, we propose and discuss a steepest descent method based on a fixed and invariant triangulation. 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One would like to use monoaxial coils measurements to obtain estimates on the clogging volume. We propose a 3D shape optimization technique based on simplified parametrization of the geometry adapted to the measurement nature and resolution. The direct problem is modeled by the eddy current approximation of time-harmonic Maxwell's equations in the low frequency regime. A potential formulation is adopted in order to easily handle the complex topology of the industrial problem setting. We first characterize the shape derivatives of the deposit impedance signal using an adjoint field technique. For the inversion procedure, the direct and adjoint problems have to be solved for each coil vertical position which is excessively time and memory consuming. To overcome this difficulty, we propose and discuss a steepest descent method based on a fixed and invariant triangulation. 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