Fast and scalable finite-element based approach for density functional theory calculations using projector augmented wave method

In this paper, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale electronic structure calculations. This real-space approach for DFT calculations combines the efficiency of PAW formalism involving smooth electronic fields with the ability of systematically improvable higher-order finite-element basis to achieve significant computational gains. In particular, we developed efficient strategies for solving the underlying FE discretized PAW generalized eigenproblem by employing the Chebyshev filtered subspace iteration approach to compute the desired eigenspace in each self-consistent field iteration. These strategies leverage the low-rank perturbation of the FE basis overlap matrix in conjunction with reduced order quadrature rules to invert the discretized PAW overlap matrix while also exploiting the sparsity of both the local and nonlocal parts of the discretized PAW Hamiltonian and overlap matrices. Further, we employ higher-order quadrature rules to accurately evaluate integrals in these matrices involving PAW-atomic data, allowing the use of coarser FE meshes for various electronic fields. Using the proposed approach, we benchmark the accuracy and performance of various representative examples involving periodic and nonperiodic systems with plane-wave-based PAW implementations. Furthermore, we also demonstrate a considerable computational advantage $(\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}\ensuremath{-}10\ifmmode\times\else\texttimes\fi{})$ over state-of-the-art plane-wave methods for medium to large-scale systems ($\ensuremath{\sim}6000\ensuremath{-}35\phantom{\rule{0.16em}{0ex}}000$ electrons). Finally, we show that our approach (PAW-FE) significantly reduces the degrees of freedom to achieve the desired accuracy, thereby enabling large-scale DFT simulations ($>50\phantom{\rule{0.16em}{0ex}}000$ electrons) at an order of magnitude lower computational cost compared to norm-conserving pseudopotential calculations using finite-element discretization.