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- W1567984031 abstract "We consider a set of parameterized planar arcs (x(t), y(t)) (0 ≤t ≤1), satisfying certain smoothness, regularity and mono- tonicity conditions (in particuler x(t) is monotone increasing, and y(t) positive and unimodal), and a functional J(y) involving an ad- justable weighting function !(t) and a positive constant � > 1. We first prove the strict convexity of the functional for � ≥ 2. Under the less stringent condition � > 1, we derive the stationarity condi- tion and the formal expression for the Hessian, and prove that if a point exists at which the functional is stationary w.r.t. variations in y = y(t), for fixed x = x(t), then it is unique and realizes a global minimum; the functional is then unimodal. We also observe that the stationarity condition (Euler-Lagrange equation) is an integral- differential equation depending only on the arc shape and not on the parameterization per se, which gives the variational problem a cer- tain intrinsic character. Then, we solve the inverse problem: given an admissible parameterized arc, we construct a smooth weighting function !(t) for which the stationarity condition is satisfied, thus making the functional unimodal, and derive certain asymptotics. A numerical example pertaining to optimum-shape design in aerody- namics is computed for illustration." @default.
- W1567984031 created "2016-06-24" @default.
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- W1567984031 date "2005-01-01" @default.
- W1567984031 modified "2023-09-28" @default.
- W1567984031 title "Inverse shape optimization problems and application to airfoils" @default.
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