论文标题
张量结构化算法，用于降低级缩放大规模kohn-sham密度理论计算
Tensor-structured algorithm for reduced-order scaling large-scale Kohn-Sham density functional theory calculations
论文作者
论文摘要
我们通过构建适合Kohn-Sham Hamiltonian的Tucker张量基构建张量张量，提出了一种张量结构化算法，以进行有效的大规模DFT计算，并以真实的空间为基础。所提出的方法使用可分离的近似值对Kohn-Sham Hamiltonian和$ L_1 $本地化技术来生成构成Tucker Tensor基础的1D局部函数。数值结果表明，所得的Tucker张量基的基础在地面能量中表现出指数收敛，而Tucker等级的增加。此外，提出的张量结构化算法显示出有或没有缝隙的两个系统的系统大小，并涉及数千个原子。这种降低的缩放比例还导致了所提出的方法的表现超过了2,000个电子的系统。
We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn-Sham Hamiltonian and an $L_1$ localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2,000 electrons.
