Efficient and accurate linear algebraic methods for large-scale electronic structure calculations with nonorthogonal atomic orbitals
Efficient and accurate linear algebraic methods for large-scale electronic structure calculations with nonorthogonal atomic orbitals
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DOI：
10.1103/physrevb.83.165103
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发表时间：
2011-01
影响因子：
3.7
通讯作者：
H. Teng;T. Fujiwara;T. Hoshi;T. Sogabe;S.-L. Zhang;S. Yamamoto
中科院分区：
文献类型：
--
作者：
H. Teng;T. Fujiwara;T. Hoshi;T. Sogabe;S.-L. Zhang;S. Yamamoto
在材料物理领域，近期出现了对大规模电子结构计算的需求，因此用于大型联立线性方程组的高效且精确的代数方法变得极为重要。我们研究了广义平移共轭正交共轭梯度法、广义兰索斯法和广义阿诺尔迪法。它们是单电子薛定谔方程大型联立线性方程组的求解方法，并将整个希尔伯特空间映射到一个称为克雷洛夫子空间的小的子空间。这些方法被应用于具有美国海军研究实验室紧束缚哈密顿量的面心立方金体系[F. 基尔希霍夫等人，《物理评论B》63，195101（2001）]。我们比较了这些方法与精确计算的结果，并表明它们具有同等的准确性。还讨论了CPU时间对体系大小的依赖关系。从CPU时间和内存大小的角度来看，广义兰索斯法和广义阿诺尔迪法最适合大规模分子动力学模拟。
The need for large-scale electronic structure calculations arises recently in the field of material physics, and efficient and accurate algebraic methods for large simultaneous linear equations become greatly important. We investigate the generalized shifted conjugate orthogonal conjugate gradient method, the generalized Lanczos method, and the generalized Arnoldi method. They are the solver methods of large simultaneous linear equations of the one-electron Schrodinger equation and map the whole Hilbert space to a small subspace called the Krylov subspace. These methods are applied to systems of fcc Au with the NRL tight-binding Hamiltonian [F. Kirchhoff et al., Phys. Rev. B 63, 195101 (2001)]. We compare results by these methods and the exact calculation and show them to be equally accurate. The system size dependence of the CPU time is also discussed. The generalized Lanczos method and the generalized Arnoldi method are the most suitable for the large-scale molecular dynamics simulations from the viewpoint of CPU time and memory size.