Formulation intégrale surfacique des équations de Maxwell pour la simulation de contrôles non destructifs par courant de Foucault. Etude préliminaire à la mise en œuvre de la méthode multipôle rapide.

Abstract : To simulate numerically a non-destructive by eddy current testing (NDT-CF), the sensor response can be modeled through a semi-analytical approach by volume integral equations. Faster than the finite element method, this approach is however restricted to the study of plane or cylindrical parts (without taking into account the edge effects) because of the complexity of the expression of the dyadic Green function for more general configurations. However, there is an industrial demand to extend the capabilities of the CF model in complex configurations (deformed plates, edges effects...). We were thus brought to formulate the electromagnetic problem differently, by setting ourselves the goal of maintaining a semi-analytical approach. The surface integral equation (SIE) expresses the volume problem by an equivalent transmission one at the interfaces (2D) between homogeneous subdomains. This problem is approached by a linear system (by the method of moments), whose number of unknowns is reduced due to the nature of the surfacic mesh. Therefore, this system can be solved by a direct solver for small configurations. That enabled us to treat several various positions of the sensor for only one inversion of the impedance matrix. The numerical results obtained using this formulation involve plates with consideration of edge effects such as edge and corner. They are consistent with results obtained by the finite element method. For larger configurations, we conducted a preliminary study for the adaptation of an acceleration method of the matrix-vector product involved in an iterative solver (fast multipole method or FMM) to define the conditions under which the FMM calculation works correctly (accuracy, convergence ...) in the NDT's domain. A special attention has been given to the choice of basis functions (which have to satisfy an Hdiv conforming property) and on the evaluation of near interactions (which are weakly singular).
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Mathematical Physics [math-ph]. Ecole Polytechnique X, 2011. French


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Contributor : Tekoing Lim <>
Submitted on : Friday, May 20, 2011 - 1:55:57 AM
Last modification on : Thursday, April 23, 2015 - 2:00:08 PM

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Tekoing Lim. Formulation intégrale surfacique des équations de Maxwell pour la simulation de contrôles non destructifs par courant de Foucault. Etude préliminaire à la mise en œuvre de la méthode multipôle rapide.. Mathematical Physics [math-ph]. Ecole Polytechnique X, 2011. French. <pastel-00594405>

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