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We present a computationally efficient approach to perform large-scaleall-electron density functional theory calculations by enriching the classicalfinite element basis with compactly supported atom-centered numerical basisfunctions that are constructed from the solution of the Kohn-Sham (KS) problemfor single atoms. We term these numerical basis functions as enrichmentfunctions, and the resultant basis as the enriched finite element basis. Theenrichment functions are compactly supported through the use of smooth cutofffunctions, which enhances the conditioning and maintains the locality of thebasis. The integrals involved in the evaluation of the discrete KS Hamiltonianand overlap matrix in the enriched finite element basis are computed using anadaptive quadrature grid based on the characteristics of enrichment functions.Further, we propose an efficient scheme to invert the overlap matrix by using ablock-wise matrix inversion in conjunction with special reduced-orderquadrature rules to transform the discrete Kohn-Sham problem to a standardeigenvalue problem. Finally, we solve the resulting standard eigenvalue problemby using a Chebyshev polynomial based filtering technique to compute therelevant eigenspectrum. We demonstrate the accuracy, efficiency and parallelscalability of the proposed method on semiconducting and heavy-metallic systemsof various sizes, with the largest system containing 8694 electrons. We obtainaccuracies in the ground-state energies that are within $\sim 1$mHa withground-state energies obtained from classical finite element as well asgaussian basis sets. We observe a $50-300$ and $\sim 8$ fold reduction in theoverall computational time when compared to classical finite element andgaussian basis, respectively. We also observe good parallel scalability up to384 processors for a benchmark system comprising of 280-atom siliconnano-cluster.

Large-scale all-electron density functional theory calculations using an enriched finite element basis