Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

Rufus, Nelson D.; Kanungo, Bikash; Gavini, Vikram

doi:10.1103/physrevb.104.085112

Cited by 12 publications

(21 citation statements)

References 87 publications

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“…al. 77 have proposed the orthogonalized enriched FE (OEFE) basis, in which, the atomic solutions are orthogonalized with respect to the underlying FE basis before augmenting as enrichments. The OEFE basis yields well-conditioned matrices ensuring numerical robustness.…”

Section: Enriched Finite Element Basismentioning

confidence: 99%

“…The OEFE basis yields well-conditioned matrices ensuring numerical robustness. However, we note that the EFE basis presented in 75 and the OEFE basis presented in 77 span the same function space. Thus, in this work we employ the following strategy to compute ionic forces and cell stresses.…”

Section: Enriched Finite Element Basismentioning

confidence: 99%

“…The EFE basis, which enriches the FE basis with compactly supported enrichment functions-such as, for e.g., those constructed from single-atom wavefunctions-can be used to significantly reduce the number of FE basis functions, and consequently improve the computational efficiency of all-electron calculations. While EFE basis has been employed for both all-electron calculations [74][75][76][77] as well as calculations involving hard pseudopotentials 78,79 , in the present work we consider the framework of all-electron density functional theory.…”

Section: Introductionmentioning

confidence: 99%

“…The formulation is closely related to a recent work by Motamarri and Gavini 1 , who proposed the configurational force approach for the FE basis. In the present work, we extend the formulation of configurational forces to the enriched FE basis proposed in 75,77 , and derive the additional contributions that arise from the atom-centered enrichment functions. An advantage of the configurational force approach is that it provides a unified framework to compute ionic forces as well as cell stresses for geometry optimization.…”

Section: Introductionmentioning

confidence: 99%

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Ionic forces and stress tensor in all-electron DFT calculations using enriched finite element basis

Rufus,

Gavini

2022

Preprint

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The enriched finite element basis-wherein the finite element basis is enriched with atom-centered numerical functions-has recently been shown to be a computationally efficient basis for systematically convergent all-electron DFT ground-state calculations. In this work, we present the expressions to compute variationally consistent ionic forces and stress tensor for all-electron DFT calculations in the enriched finite element basis. In particular, we extend the formulation of configurational forces in [Motamarri & Gavini (2018)] 1 to the enriched finite element basis and elucidate the additional contributions arising from the enrichment functions. We demonstrate the accuracy of the formulation by comparing the computed forces and stresses for various benchmark systems with those obtained from finite-differencing the ground-state energy. Further, we also benchmark our calculations against Gaussian basis for molecular systems and against the LAPW+lo basis for periodic systems.

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Section: Enriched Finite Element Basismentioning

confidence: 99%

Section: Enriched Finite Element Basismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ionic forces and stress tensor in all-electron DFT calculations using enriched finite element basis

Rufus,

Gavini

2022

Preprint

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“…We remark that a similar smeared nuclear charges strategy has also been adopted in a recent work [35], involving enriched finite-elements for solution of all-electron Kohn-Sham DFT equations. Finally, incorporating the functional derivative of the local reformulation of the electrostatic energy with smeared nuclear charges in Eq.…”

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confidence: 99%

DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization

Das,

Motamarri,

Subramanian

et al. 2022

Preprint

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We present DFT-FE 1.0, building on DFT-FE 0.6 [Comput. Phys. Commun. 246, 106853 (2020)], to conduct fast and accurate large-scale density functional theory (DFT) calculations (reaching ∼ 100, 000 electrons) on both many-core CPU and hybrid CPU-GPU computing architectures. This work involves improvements in the real-space formulation-via an improved treatment of the electrostatic interactions that substantially enhances the computational efficiency-as well highperformance computing aspects, including the GPU acceleration of all the key compute kernels in DFT-FE. We demonstrate the accuracy by comparing the ground-state energies, ionic forces and cell stresses on a wide-range of benchmark systems against those obtained from widely used DFT codes. Further, we demonstrate the numerical efficiency of our implementation, which yields ∼ 20× CPU-GPU speed-up by using GPU acceleration on hybrid CPU-GPU nodes. Notably, owing to the parallel-scaling of the GPU implementation, we obtain wall-times of 80−140 seconds for full groundstate calculations, with stringent accuracy, on benchmark systems containing ∼ 6, 000 − 15, 000 electrons.

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Accurate Approximations of Density Functional Theory for Large Systems with Applications to Defects in Crystalline Solids

Bhattacharya

Gavini

Ortiz

et al. 2022

Density Functional Theory

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This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in other applications. The key idea is to formulate DFT as a minimization problem over the density operator, and to cast spatial and spectral discretization as systematically convergent approximations. This enables efficient and adaptive algorithms that solve the equations of DFT with no additional modeling, and up to desired accuracy, for very large systems, with linear and sublinear scaling. Various approaches based on such approximations are presented, and their numerical performance demonstrated through selected examples. These examples also provide important insight about the mechanics and physics of defects in crystalline solids.

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Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

Cited by 12 publications

References 87 publications

Ionic forces and stress tensor in all-electron DFT calculations using enriched finite element basis

Ionic forces and stress tensor in all-electron DFT calculations using enriched finite element basis

DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization

Accurate Approximations of Density Functional Theory for Large Systems with Applications to Defects in Crystalline Solids

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