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Theses

Développement d'outils d'optimisation pour freefem++

Abstract : The goal of this Ph.D. thesis was the development of tools for the FreeFem++ software in order to make optimization problems easier to deal with. This has been accomplished following two main directions. Firstly, a set of optimization softwares is interfaced and validated before making use of them. Then, we analyse the field of automatic differentiation as a potential mean of simplification for the users. FreeFem++ is an integrated development environment dedicated to numerically solving partial differential equations. Its high level language allows the user for a comfortable experience while using its mesh generation capabilities, linear system solvers, as well as finite elements capabilities. We describe the newly available optimization features, with a certain emphasis on the open source software IPOPT, which implements a state of the art interior points method for large scale optimization. These optimization tools are then used in a set of quite successful applications, among which minimal surfaces, Bose-Einstein condensate simulation, and an inverse positioning problem in the context of computational fluid dynamics. Finally, after an introduction to the techniques of algorithmic differentiation, we also present an unstable prototype version of FreeFem++ including automatic differentiation features.
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Submitted on : Wednesday, June 4, 2014 - 4:02:28 PM
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Sylvain Auliac. Développement d'outils d'optimisation pour freefem++. Mathématiques générales [math.GM]. Université Pierre et Marie Curie - Paris VI, 2014. Français. ⟨NNT : 2014PA066035⟩. ⟨tel-01001631⟩

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