Improvement of a domain decomposition method for electronic structures calculation

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. (author)