The possibility to compute first- and second-derivatives of functionals subject to equality constraints given by state equations (and in particular non-linear systems of Partial Derivative Equations) allows us to use efficient techniques to solve several industrial-strength problems. Among possible applications that require knowledge of the derivatives, let us mention: aerodynamic shape optimization with gradient-based descent algorithms, propagation of uncertainties using perturbation techniques, robust optimization, and improvement of the accuracy of a functionnal using the adjoint state. In this work, we develop and analyze several strategies to evaluate the first- and second-derivatives of constrained functionals, using techniques based on Automatic Differentiation. Furthermore, we propose a descent algorithm for aerodynamic shape optimization, that is based on techniques of multi-level gradient, and which can be applied to different kinds of parameterization.
Sensitivity Evaluation in Aerodynamic Optimal Design / Martinelli, Massimiliano; relatore esterno: Beux, François; Scuola Normale Superiore, 2007.
Sensitivity Evaluation in Aerodynamic Optimal Design
Martinelli, Massimiliano
2007
Abstract
The possibility to compute first- and second-derivatives of functionals subject to equality constraints given by state equations (and in particular non-linear systems of Partial Derivative Equations) allows us to use efficient techniques to solve several industrial-strength problems. Among possible applications that require knowledge of the derivatives, let us mention: aerodynamic shape optimization with gradient-based descent algorithms, propagation of uncertainties using perturbation techniques, robust optimization, and improvement of the accuracy of a functionnal using the adjoint state. In this work, we develop and analyze several strategies to evaluate the first- and second-derivatives of constrained functionals, using techniques based on Automatic Differentiation. Furthermore, we propose a descent algorithm for aerodynamic shape optimization, that is based on techniques of multi-level gradient, and which can be applied to different kinds of parameterization.File | Dimensione | Formato | |
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Martinelli_Massimiliano.pdf
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Descrizione: doctoral thesis full text
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Tesi PhD
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8.73 MB
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8.73 MB | Adobe PDF |
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