Large-scale Real-space Kohn-Sham Density Functional Theory Calculations Using Adaptive Finite-element Discretization.

Past few decades have seen an increasingly important role played by quantum mechanical calculations based on Kohn-Sham density functional theory (DFT) in the investigation of wide variety of materials properties. However, large-scale DFT calculations are computationally very demanding and hence have been primarily associated with either plane-wave basis or atomic-orbital basis sets, imposing severe restrictions on the permissible boundary conditions and the type of materials systems simulated. On the other hand, finite-element (FE) discretization of DFT, among the real-space techniques is versatile and is amenable for unstructured coarse-graining, allows for consideration of complex geometries and boundary conditions, and further is scalable on parallel computing platforms. However, the inherent shortcomings in the use of finite-element discretization for DFT have made it less attractive for large-scale simulations restricting the materials system sizes to few hundreds of electrons. This thesis addresses the inherent shortcomings and presents the development of new computationally efficient and robust parallel algorithms to enable large-scale DFT simulations using finite-element basis (DFT-FE). The proposed DFT-FE enabled for the first time, simulation of electronic structure of materials systems as large as 7000 atoms (14000 valence electrons) using finite-element basis. The key ideas in the development of DFT-FE include (i) an adaptive higher-order spectral finite-element based self-consistent framework which can handle all-electron and pseudopotential calculations with complex boundary conditions on a single footing, (ii) a subspace projection method to reduce the computational complexity of DFT calculations while treating metallic and insulating systems in a single finite-element framework and (iii) a configurational force approach to efficiently compute forces on atoms to find the geometry of a given materials system in the most stable state. The numerical investigations conducted with DFT-FE on representative benchmark examples show that computational efficiency of finite-element basis is competing with commercial codes using other basis sets and show excellent parallel scalability. Furthermore, the benchmark studies involving pseudopotential calculations on systems up to 14000 electrons as well as all-electron calculations on systems up to 4000 electrons, revealed that the proposed subspace projection algorithm scales sub-quadratically with system size resulting in excellent chemical accuracies at reduced computational cost.