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Amélioration d'une méthode de décomposition de domaine pour le calcul de structures électroniques

Guy Bencteux 1, 2
1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : This work is about a domain decomposition method for electronic structure computations, with Hartree-Fock or DFT (Density Functional Theory) models. Usually, the numerical simulation of these models involve the solution of a generalized eigenvalue problem, which is a bottleneck due to the cubic scaling of the number of operations. The MDD (Multilevel Domain Decomposition) method, that have been introduced in a previous PhD (Maxime Barrault, 2005), replace the generalized eigenvalue problem with a constrained minimization problem, for which it is easier to take benefit of the localization properties of the solution. Results produced by the present work are : * the numerical analysis of the algorithm : a local convergence result has been proved, on a simplified instance of the problem that exhibits the same mathematical difficulties; * improvement of speed and accuracy, with one-dimensional sub-domain arrangements, as well as demonstration of scalability up to one thousand processors; * extension of the algorithm and its numerical implementation to cases with 2D/3D subdomains arrangement.
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Submitted on : Monday, June 15, 2009 - 9:57:29 PM
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Guy Bencteux. Amélioration d'une méthode de décomposition de domaine pour le calcul de structures électroniques. Mathématiques [math]. Ecole des Ponts ParisTech, 2008. Français. ⟨tel-00391801v2⟩

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