Déformations libres de contours pour l’optimisation de formes et application en électromagnétisme

Abstract : We develop a deformation technique for shape optimization problems. The shapes are described only by their boundary, parameterized by piecewise Bézier curves. They are polynomial curves hence entirely defined by their coefficients which are called control points. By moving these control points the curves change and so is the boundary of the shape. Used in a shape optimization problem, the control points become the optimization variables meaning that the problem is a parametric optimization problem. Our method consists in first parameterizing the boundary of a shape by Bézier curves as stated above and then compute a deformation of the control points from a descent direction for the objective function. The method is almost purely geometric but we add a way to include topological changes by diving a shape into two or conversly merging two shapes into one. We tested our method on three particular shape optimization problems which are microwave filter design, inclusions detection and optimal trajectories.
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Pierre Bonnelie. Déformations libres de contours pour l’optimisation de formes et application en électromagnétisme. Optimisation et contrôle [math.OC]. Université de Limoges, 2017. Français. ⟨NNT : 2017LIMO0006⟩. ⟨tel-01635246⟩

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