We describe the development and example applications of multigrid methodology in large-scale, massively parallel DFT calculations. A real-space grid is used as a basis, together with a compact Mehrstellen discretization for the differential operators. The computational procedures are very stable and efficient, due to the automatic preconditioning and convergence acceleration implicit in the multigrid method, and the high accuracy of the discretization, which conserves the total energy to the level of microvolts per atom in large-scale quantum molecular dynamics simulations. We have also reformulated this approach in terms of variationally-optimized localized orbitals, which reduce the scaling of the most expensive parts of the calculation to O(N) and enables calculations for over a thousand atoms. The optimized-orbital method has been combined with an efficient Green's function technique for evaluating the quantum conductance in a localized basis, enabling nearly O(N) calculations of quantum transport.
We have applied the above methodology to a wide range of problems in condensed matter physics. Several examples will be briefly described during the talk, including the properties of nanotubes and polarization in BN/C systems, optical properties of surfaces (including GW corrections), and quantum transport in nanotube-based devices and nanotube/cluster sensor assemblies.
This is joint work with E. L. Briggs, M. Buongiorno Nardelli, J.-L. Fattebert, V. Meunier, S. Nakhmanson, W. G. Schmidt, and Q. Zhao.
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