Optimization on Shape Manifolds with Fluid-Mechanical Applications under Uncertainty
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Shape optimization algorithms are commonly applied in order to improve structural parts in both the academic as well as the industrial field. Exploiting the Riemannian manifold structure of spaces in which each element represents a shape, so-called shape spaces, allows the formulation of the optimization problem in a continuous sense, which—together with, e.g., known convergence properties—also yields mesh independence of the result of the optimization. However, if the problem is subject to uncertainty, then this further complicates the optimization and will be focus of this presentation. The theoretical framework for optimization on shape manifolds under uncertainty is described and the application of this framework for the optimization of shapes in a fluid-mechanical problem is shown.
