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Méthodes hiérarchiques pour l'optimisation géométrique de structures rayonnantes

Benoît Chaigne 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : A reflector antenna is a device that is widely use for satellite communication. The life length of such a device depends highly on the fatigue due to the energy consumption for the signal emission. Thus, one of the goals of the optimal design of an antenna is to improve the productivity of systems designed for a given task, for a fixed input power. A reflector antenna is characterized by radiating surfaces whose geometry is the main parameter that can be controled to fulfill the task. Based on the time-harmonic wave propagation simulation in free space, numerical procedures for the optimal design of the shape of radiating structures are examined. Namely, we aim at minimizing a criterion that represents the task in mathematical terms. In this framework, classical optimization methods are often submitted to challenging difficulties related to the fact that the problems are ill-posed because multimodal and numerically stiff. Since the control is the geometry of the reflectors, we have investigated in this thesis the potential enhancements of basic algorithms using hierarchical parametric representations. The theoretical foundations of the proposed algorithms rely on the Multigrid methods for solving PDE. A theoretical example for shape optimization is considered in order to derive different multilevel strategies. These strategies are then applied to real-case problems for the optimal design of reflector antennas. Numerical experiences show that basic algorithms are effectively enhanced in terms of robustness and convergence rate.
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Submitted on : Monday, November 2, 2009 - 4:13:43 PM
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Benoît Chaigne. Méthodes hiérarchiques pour l'optimisation géométrique de structures rayonnantes. Sciences de l'ingénieur [physics]. Université Nice Sophia Antipolis, 2009. Français. ⟨tel-00429366⟩

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