Artificial boundary conditions for axisymmetric eddy current probe problems

Haddar, Houssem; Jiang, Zixian; Lechleiter, Armin

doi:10.1016/j.camwa.2014.10.008

Cited by 8 publications

(12 citation statements)

References 15 publications

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“…The result follows directly from combining those for non-linear magneto-statics in [51] with the results for non-linear problems in unbounded domains [23]. If in addition we had Ω Fe = ∅ we would end up with an even simpler linear elliptic 185 problem, for which existence and uniqueness are immediately available [31,30]. Rigorous existence and uniqueness assertion for the general case are still an open problem.…”

Section: Weak Formulationmentioning

confidence: 92%

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Heumann

Rapetti

2017

Journal of Computational Physics

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International audienceExisting finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping

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Section: Weak Formulationmentioning

confidence: 92%

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Heumann

Rapetti

2017

Journal of Computational Physics

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“…+ ) being the unique solution of (4) with source term defined by (11) replacing u 0 by the function v ∈ L 2 (D). We first prove the following important properties of the operator S. Lemma 3.…”

Section: Foundations Of the Linear Sampling Methods And Algorithmmentioning

confidence: 99%

“…We formalize this setting in an axisymmetric configuration of the medium and for the eddy current model. Our analysis of the forward problem follows [11,2]. We then study the theoretical foundations of the LSM in the case where the deposit is characterized by a change in the conductivity with respect to a reference configuration.…”

Section: Introductionmentioning

confidence: 99%

Near-Field Linear Sampling Method forAxisymmetric Eddy Current Tomography

Haddar,

Riahi

2021

Preprint

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This paper is concerned with Eddy-Current (EC) nondestructive testing of conductive materials and focuses, in particular, on extending the well-known Linear Sampling Method (LSM) to the case of EC equations. We first present the theoretical foundation of the LSM in the present context and in the case of point sources. We then explain how this method can be adapted to a realistic setting of EC probes. In the case of identifying the shape of external deposits from impedance measurements taken from inside of the tube (steam generator), we show how the method can be applied to measurements obtained from a sweeping set of coils. Numerical experiments suggest that good results can be achieved using only a few coils and even in the limiting case of backscattering data.

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“…In previous studies, we modeled the axisymmetric eddy current problem with an efficient finite element approximation which involves artificial boundary conditions to cut off the computational domain and thus reduce the numerical cost (see [10]). Based on this model an inversion algorithm has been developed using shape optimization methods to reconstruct the shape of some clogging magnetite deposits [12].…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models

Haddar

Jiang

2015

Inverse Problems

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Thin copper deposits covering the steam generator tubes can blind eddy current probes in non-destructive testings of problematic faults and it is therefore important that they are identified. Existing methods based on shape reconstruction using eddy current signals encounter difficulties of high numerical costs due to the layer's small thickness and high conductivity. In this article, we approximate the axisymmetric eddy current problem with some appropriate asymptotic models using effective transmission conditions representing the thin deposits. In these models, the geometrical information related to the deposit is transformed into parameter coefficients on a fictitious interface. A standard iterative inversion algorithm is then applied to the asymptotic models to reconstruct the thickness of the thin copper layers. Numerical tests both validating the asymptotic model and showing the benefits of the inversion procedure are provided.

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Artificial boundary conditions for axisymmetric eddy current probe problems

Cited by 8 publications

References 15 publications

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

Near-Field Linear Sampling Method forAxisymmetric Eddy Current Tomography

Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models

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