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International audience; A fast and general Partial Element Equivalent Circuit (PEEC) method based on the Fast-Fourier-Transform (FFT) is proposed for the first time. The numerical tool only requires common CAD data input files (e.g. .stl format), then the discretization process is performed automatically by means of a fast voxelization technique based on ray intersection, thus drastically reducing the human effort required to setup the model. The method allows for considering at the same time inductive and capacitive effects, and is focused on power electronics applications where propagation effects can be neglected, whereas all the other electromagnetic phenomena are considered. Specifically, the proposed method is particularly suited for problems where both electric and magnetic fields are equally important and therefore quasistatic approximations do not apply. An ad-hoc preconditioner which significantly speeds-up the solver is also proposed and, thanks to the FFT, both memory and computation time are significantly reduced, without the need of applying data compression. Both linear and non-linear materials are considered by the proposed FFT-PEEC method. Sample implementation of the method is made publicly available.

This paper presents a model based procedure for in situ error compensation of magnetic measurements in fusion experiments. The proposed approach is validated on RFX-mod2, a toroidal device presently being upgraded with a sophisticated new magnetic diagnostic system and a state-of-the-art real time control system. The numerical simulations are performed with the code CAFE-VI; synthetic measurements are used to assess the reliability of the proposed method.

The main focus of this thesis is to extend and improve the applicability and the accuracy of the Unstructured Partial Element Equivalent Circuit (PEEC) method. The interest on this argument is spurred by the growing need of fast and efficient numerical methods, which may help engineers during the design and other stages of the production of new generation electric components.First, the PEEC method in its unstructured form is extended to magnetic media. In this regard, two formulations are developed and compared: the first, based on the Amperian interpretation of the magnetization phenomena, is derived from the existing literature concerning the standard (structured) version of PEEC; the second, based on the Coulombian interpretation of the magnetization phenomena, is proposed by the author with the aim of collocating PEEC in the context of Volume Integral Equation methods.Then, the coupling of PEEC with low-rank compression techniques is investigated. Two different methods are applied: the first is based on hierarchical matrices (H and H2 matrices) while the second is based on hierarchical-semi-separable (HSS) matrices. The two methods are compared and the main numerical issues which emerge by applying low-rank techniques to PEEC are analyzed.Finally, the developed unstructured PEEC method is combined withthe Marching On-in-Time scheme for the study of fast transient phenomena with a rich harmonic content. Moreover, two different stochastic PEEC methods are developed for uncertainty quantification analysis. The first is based on the Polynomial Chaos expansion while the second is based on the Parametric Model Order Reduction technique coupled with spectral expansion., L'objectif principal de cette thèse est d'étendre et d'améliorer la précision de la méthode des circuits équivalents à éléments partiels non structurés (Unstructured PEEC). L'intérêt pour ce sujet est stimulé par le besoin croissant de méthodes numériques rapides et efficaces, qui peuvent aider les ingénieurs pendant la conception et les autres phases de la production de composants électriques et électroniques de nouvelle génération.Dans un premier temps, la méthode PEEC sous sa forme non structurée est étendue aux supports magnétiques. Deux formulations sont développées et comparées: la première, basée sur l'interprétation ampérienne des phénomènes d’aimantation, provient de la littérature relative à la version standard (structurée) de la méthode PEEC. La seconde, basée sur l'interprétation Coulombienne des phénomènes d’aimantation, est proposée par l'auteur dans le but de recentrer la méthode PEEC dans le contexte des méthodes d'intégrale de volume (Volume Integral Equation).Dans un deuxième temps, les travaux portent sur l’utilisation de techniques de compression de bas rang afin de résoudre efficacement les problèmes de PEEC et de préserver le temps et la mémoire de calcul. Deux méthodes différentes sont appliquées: la première est basée sur des matrices hiérarchiques (matrices H et H2), tandis que la seconde repose sur des matrices hiérarchiques semi-séparables (HSS). Les deux méthodes sont comparées et les principaux problèmes numériques qui se posent en appliquant ces techniques de compression de bas rang à la méthode PEEC sont analysés.La méthode PEEC non structurée est ensuite combinée à l’approche Marching On-In Time (MOT) pour l’étude des phénomènes transitoires rapides avec un contenu harmonique riche.Enfin, deux méthodes PEEC stochastiques différentes ont été développées pour la quantification des incertitudes. La première est basée sur l'expansion Polynomial Chaos, tandis que la seconde repose sur la technique de réduction de l'ordre du modèle paramétrique (Parametric Model Order Reduction) combinée à une expansion spectrale.