Sensitivity Evaluation in Aerodynamic Optimal Design
Massimiliano Martinelli
(INRIA, BP93, 06902 Sophia-Antipolis, France)
PhD thesis, Scuola Normale Superiore di Pisa and University of Nice, 2007 (198 pages)
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.
Keywords:
Derivatives, Second Derivatives, Constrained Functionals,
Constrained Optimization, Shape Optimization, Robust Optimization,
Automatic Differentiation, Scientific Computing,
Gradient, Adjoint Models.
@phdthesis{phdMartinelli07,
author = {Martinelli, M.},
title = {Sensitivity Evaluation in Aerodynamic Optimal Design},
type = {PhD},
school = {Scuola Normale Superiore di Pisa and Universit{\'e} de Nice Sophia-Antipolis},
year = 2007
}