稀疏SCF算法及其并行实现：在DFTB中的应用
A Sparse SCF algorithm and its parallel implementation: Application to DFTB
摘要：
我们提出了一个算法和它的并行实现解决Hartree-Fock或密度泛函理论中遇到的自洽问题。该算法利用矩阵的稀疏性，通过使用本地分子轨道。该实现允许有效地利用现代对称多处理（SMP）计算机体系结构。作为第一个应用程序，该算法被用于密度泛函的紧束缚方法，其中大部分的计算时间是花在线性代数例程（对角化的Fock/Kohn-Sham矩阵）。我们表明，与此算法（i）单点计算非常大的系统（数百万个原子）可以在大型SMP机器上执行（ii）涉及中等规模系统的计算（1~000- 100万个原子）也有很强的加速能力，可以在标准服务器上有效地运行。可以控制分子轨道系数的偏离，使得它保持小于SCF收敛标准。
英文摘要：
We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density functional based tight binding method, for which most of the computational time is spent in the linear algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that with this algorithm (i) single point calculations on very large systems (millions of atoms) can be performed on large SMP machines (ii) calculations involving intermediate size systems (1~000--100~000 atoms) are also strongly accelerated and can run efficiently on standard servers (iii) the error on the total energy due to the use of a cut-off in the molecular orbital coefficients can be controlled such that it remains smaller than the SCF convergence criterion.
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