Algorithmes multigrilles adaptatifs et scalables

Abstract : In many industrial activities such as aeronautics, space industry, oil industry and many others, it is essential to carry out numerical computations to simulate phenomena occurring in natural or artificial systems modelisable by mechanical Continuum. This thesis focuses on the following scientific question: how, for a given simulation and computing means given, obtain the highest prediction accuracy? Our contribustion makes the link between two numerical simulation techniques: multigrid methods and new recently developed anisotropic adaptative methods. We solve an elliptic partial differential equation. The adaptation of the mesh to the given problem is based on minimization of a given magnitude following the adaptation method employed: the interpolation error for the Hessian-based adaptation, a weighting of the approximation error for goal-oriented method and the norm of the approximation error for the norm-oriented method. The multigrid method permits to accelerate convergence on each mesh. Several tests cases were carried out to ensure the effectiveness of the different methods.
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Gautier Brèthes. Algorithmes multigrilles adaptatifs et scalables. Mathématiques générales [math.GM]. Université Nice Sophia Antipolis, 2015. Français. ⟨NNT : 2015NICE4103⟩. ⟨tel-01256185v2⟩

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