Multilevel domain decomposition for electronic structure calculations

We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of domain decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains containing up to 40,000 atoms and 200,000 atomic orbitals. Both the computational cost and the memory requirement scale linearly with the number of atoms. Additional speed-up can easily be obtained by parallelization. We show that this domain decomposition method outperforms the Density Matrix Minimization (DMM) method for poor initial guesses. Our method provides an efficient preconditioner for DMM and other linear scaling methods, variational in nature, such as the Orbital Minimization (OM) procedure.