BRUNELLE, M. Gaspard (2025) H-Based Boundary Integral Formulation for Eddy-Current Problems PFE - Projet de fin d'études, ENSTA.

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Résumé

The H-based variational formulation for the magneto-quasistatic eddy current model relies on functions in H(curl, Ω) with vanishing rotation in the non-conducting region ΩI . In ΩI such functions can be represented by means of scalar magnetic potentials provided that the first Betti number β1(ΩI) of ΩI vanishes, that is, ΩI has no handles. Otherwise, the use of scalar potentials entails introducing cuts Σ, such that β1(ΩI \ Σ = 0). Generically, the H-based boundary element formulation of the eddy current model involves boundary integral equations (BIEs) posed on ∂ΩI∪Ω, though the cuts contribute only a minimal amount of information, a single scalar per connected component. We investigate modifications of those BIE, which no longer rely on cuts as integration domains and only need knowledge of boundaries of cuts. For Galerkin BEM this has the big benefit that we can dispense with both construction and meshing of cuts; boundaries of cuts are just closed curves and can be built and handled much more easily.

Type de document:Rapport ou mémoire (PFE - Projet de fin d'études)
Mots-clés libres:Boundary element methods, Cutting surface, Eddy current problem, H based problem, Calderon identity, Current loop exciting field, Numerical analysis, Error convergence
Sujets:Mathématiques et leurs applications
Code ID :10832
Déposé par :Gaspard BRUNELLE
Déposé le :08 oct. 2025 09:40
Dernière modification:08 oct. 2025 14:13

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