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Méthodes d'accéleration pour la résolution numérique en électrolocation et en chimie quantique

Abstract : This thesis tackle two different topics.We first design and analyze algorithms related to the electrical sense for applications in robotics. We consider in particular the method of reflections, which allows, like the Schwartz method, to solve linear problems using simpler sub-problems. These ones are obtained by decomposing the boundaries of the original problem. We give proofs of convergence and applications. In order to implement an electrolocation simulator of the direct problem in an autonomous robot, we build a reduced basis method devoted to electrolocation problems. In this way, we obtain algorithms which satisfy the constraints of limited memory and time resources. The second topic is an inverse problem in quantum chemistry. Here, we want to determine some features of a quantum system. To this aim, the system is ligthed by a known and fixed Laser field. In this framework, the data of the inverse problem are the states before and after the Laser lighting. A local existence result is given, together with numerical methods for the solving.
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Submitted on : Monday, January 11, 2016 - 11:12:06 AM
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  • HAL Id : tel-01253674, version 1


Philippe Laurent. Méthodes d'accéleration pour la résolution numérique en électrolocation et en chimie quantique. Automatique / Robotique. Ecole des Mines de Nantes, 2015. Français. ⟨NNT : 2015EMNA0122⟩. ⟨tel-01253674⟩



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