Higher-order adaptive finite-element methods for Kohn-Sham density functional theory

JOURNAL OF COMPUTATIONAL PHYSICS

卷:253

Article

Motamarri, P.¹  Nowak, M. R.²  Leiter, K.³  Knap, J.³  Gavini, V.¹ 

[1] Univ Michigan, Dept Mech Engn, Ann Arbor, MI 48109 USA

[2] Univ Michigan, Dept Elect Engn, Ann Arbor, MI 48109 USA

[3] US Army Res Labs, Aberdeen Proving Ground, MD 21001 USA

关键词: Real space;    Density functional theory;    Finite elements;    Spectral elements;    Higher-order;    h-p refinement;    Computational efficiency;    Convergence;    Mesh adaption;    Scalability;   

DOI  :  10.1016/j.jcp.2013.06.042

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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