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

In this work, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with finite-element (FE) basis to enable accurate and large-scale electronic structure calculations. This is achieved through the synergy of the PAW method's ability to transform the underlying all-electron DFT problem into a form that involves smoother electronic fields and the potential of systematically convergent higher-order finite-element basis to achieve significant computational gains. In particular, we employ higher-order quadrature rules to evaluate integrals involving PAW-atomic data accurately, allowing the use of coarser FE meshes for electronic fields. Further, we have developed efficient computational strategies for solving the underlying FE discretized PAW generalized eigenproblem by employing the Chebyshev filtered subspace iteration approach to compute the desired eigen spectrum in each self-consistent field iteration. These strategies leverage the low-rank perturbation of FE basis-overlap to invert FE discretized PAW overlap matrix in conjunction with exploiting the FE-cell level structure of both the local and nonlocal parts of the discretized PAW Hamiltonian and overlap matrices. Using the proposed approach we benchmark the accuracy and performance on various representative examples involving periodic and non-periodic systems with state-of-the-art plane wave based PAW implementations. Furthermore, we also demonstrate a significant computational advantage over state-of-the-art plane-wave basis for large-scale systems comprising of around 35,000 electrons. Our approach (PAW-FE) significantly reduces the degrees of freedom required to achieve desired accuracy when compared to norm-conserving pseudopotentials, thereby enabling large-scale DFT simulations at an order of magnitude lower computational cost.