Titlebook: Optimal Control of PDEs under Uncertainty; An Introduction with Jesús Martínez-Frutos,Francisco Periago Esparza Book 2018 The Author(s), un

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Mathematical Preliminaires,nder uncertainty. We start with a few basic definitions and general notations. Then, some material on tensor product of Hilbert spaces is reviewed. Finally, the numerical approximation of random fields by using Karhunen-Loève expansions is studied.

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Mathematical Analysis of Optimal Control Problems Under Uncertainty,ational theory of deterministic PDEs is extended to the case of random PDEs. This variational theory may be developed by using either the formalism of tensor product of Hilbert spaces or abstract functions, i.e., functions with values in Banach or Hilbert spaces. However, tensor products of Hilbert

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Numerical Resolution of Robust Optimal Control Problems,timal control problems presented in the preceding chapters. In both cases, the main difficulty arises in the numerical approximation of statistical quantities of interest associated to solutions of random PDEs. To handle this issue, it is assumed that the random inputs of the underlying PDEs depend

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Numerical Resolution of Risk Averse Optimal Control Problems,em ., as defined in Sect. 2.2. The numerical approximation of the associated statistics combines an adaptive, anisotropic, non-intrusive, Stochastic Galerkin approach for the numerical resolution of the underlying state and adjoint equations with a standard Monte-Carlo (MC) sampling method for numer

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Structural Optimization Under Uncertainty,ng, the structural optimization problem amounts to finding the optimal distribution of material within a design domain such that a certain objective function or mechanical criterion is minimized. To ensure robustness and reliability of the final designs, a number of uncertainties should be accounted

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Jesús Martínez-Frutos,Francisco Periago EsparzaStile, purer Wille. Das sind zwei ganz verschiedene Wege. Der eine: Menschen bauen aus Sehnsucht liebevoll gemeinsam etwas für alle. Der an- re: Ein Wille managt vielf?ltige Ressourcen zu einem geplanten Ziel. Wikis sind Werkzeuge, mit denen viele Menschen mit einem Mi- mum an Organisation, Planung,

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