Contribution à l'analyse numérique de quelques problèmes en chimie quantique et mécanique.

Abstract : This thesis focuses on the numerical analysis of nonlinear eigenvalue problem, as in quantum chemistry or mechanics. Since solving them is quite expensive. We provide new methods to simplify this computation. The numerical analysis is necessary to understand the effect of this simplification on the accuracy of the result. First, we establish some {\it a priori} errors estimates of the discretization of for variational approximations of the ground state energy, eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems. Then, we focus on the analysis of the planewave discretization of the Thomas-Fermi-Von-Weizacker model. Since our objective is to gain in time computation, we provide the numerical analysis of two-grid scheme for a nonlinear eigenvalue problem. The reduced basis method may be successful in this frame and recent progress have permitted to make the computations reliable thanks to {\em a posteriori} estimators to extend the method to non linear problems. However, it may not always be possible to use the code to perform all the ``off-line'' computations required for an efficient performance of the reduced basis method. We propose, in the second part, an alternating approach based on a coarse grid finite element the convergence of which is accelerated through the reduced basis and an improved post processing.
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Submitted on : Tuesday, February 23, 2010 - 1:17:37 PM
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Rachida Chakir. Contribution à l'analyse numérique de quelques problèmes en chimie quantique et mécanique.. Modélisation et simulation. Université Pierre et Marie Curie - Paris VI, 2009. Français. ⟨tel-00459149⟩

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