Real-space finite-element-based methodologies for large-scale ab initio calculations using Projected Augmented Wave (PAW) formalism in density functional theory*

Addressing intricate challenges in complex materials problems using ab initio calculation requires significantly large length scales  and longer time scales, demanding enormous computational resources with the current state-of-the-art density functional theory(DFT) codes. Towards this, we introduce systematically convergent and scalable real space finite-element-based methodologies for projector augmented wave (PAW) formalism in DFT. 

 In particular, we propose a local real-space formulation amenable to spectral finite-element discretization of PAW formalism. Subsequently, we develop efficient HPC-centric implementation methodologies combining the ideas of low-rank perturbation of identity and mixed precision arithmetic in conjunction with Chebyshev Filtered subspace iteration approaches to solve the underlying FE discretized PAW generalized eigenproblem. We subsequently benchmark the accuracy and performance of our methodology across diverse benchmark systems involving tens of thousands of electrons on multi-node CPU and GPU architectures. We finally demonstrate that our framework facilitates a substantial reduction in the degrees of freedom to achieve the required chemical accuracy while accommodating generic boundary conditions, thereby enabling faster and more accurate large-scale DFT simulations than possible today.