Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 253, Issue -, Pages 308-343Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.06.042
Keywords
Real space; Density functional theory; Finite elements; Spectral elements; Higher-order; h-p refinement; Computational efficiency; Convergence; Mesh adaption; Scalability
Funding
- National Science Foundation [1053145, OCI-1053575]
- Army Research Office [W911NF-09-0292]
- Air Force Office of Scientific Research [FA9550-09-1-0240, FA9550-13-1-0113]
- Alexander von Humboldt Foundation
- Directorate For Engineering [1053145] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn [1053145] Funding Source: National Science Foundation
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We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings of the order of 1000-fold relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed high-erorder finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors. (C) 2013 Elsevier Inc. All rights reserved.
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