Barrault, Maxime (2005) Development of fast methods for electronic structure calculations. PhD thesis, ENPC.

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Abstract

We investigate in this thesis some approaches for the acceleration of electronic structure calculations in ab initio simulation of molecular systems.
Chapter 1 is a general introduction to the models and methods. Chapter 2 is dedicated to a mathematical description of the construction of pseudo-potentials which allow a significant reduction of the dimension of the electronic problem.
We then turn to the resolution of the generalized eigenvalue problem which is the bottleneck of the resolution of the electronic problem. In chapter 3, a multilevel domain decomposition method, scaling linearly with respect to the size of the system, is proposed for the treatment of insulators. It overcomes some drawbacks of the existing methods. Chapter 4 presents an attempt to adapt the SO called projection methods to the treatment of metallic systems.
Chapter 5 is devoted to the adaptation of the reduced basis method to the electronic problem. First, some preliminary results have been obtained on the systems H2+ and H2 using a Galerkin basis for the resolution of the electronic problem which depends on the positions of the nuclei, parameters of the system. These results demonstrate the feasibility of the approach. Second, a strategy for the treatment of a general nonlinear problem is presented.
Finally, some general conclusions about ail the approaches studied in the thesis are presented in Chapter 6, along with some tracks for further research.

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