Contributions à l'amélioration de la performance des conditions aux limites approchées pour des problèmes de couche mince en domaines non réguliers

Abstract : Transmission problems with thin layer are delicate to approximate numerically, because of the necessity to build meshes on the scale of the thin layer. It is common to avoid these difficulties by using problems with approximate boundary conditions — also called impedance conditions. Whereas the approximation of transmission problems by impedance problems turns out to be successful in the case of smooth domains, the situation is less satisfactory in the presence of corners and edges. The goal of this thesis is to propose new impedance conditions, more efficient, to correct this lack of performance. For that purpose, the asymptotic expansions of the various models -problems are built and studied to locate exactly the origin of the loss, in connection with the singular profiles associated to corners and edges. New impedance conditions are built, of multi-scale Robin or Venctel types. At first studied in dimension 2, they are then generalized in certain situations in dimension 3. Simulations have been carried out to confirm the efficiency of the theoretical methods to some.
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Submitted on : Wednesday, October 10, 2018 - 4:41:06 PM
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Alexis Auvray. Contributions à l'amélioration de la performance des conditions aux limites approchées pour des problèmes de couche mince en domaines non réguliers. Autre. Université de Lyon, 2018. Français. ⟨NNT : 2018LYSEC018⟩. ⟨tel-01892574⟩

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