论文标题
有效的并行线性缩放方法，以获取全电子真实空间密度函数扰动理论中的响应密度矩阵
Efficient Parallel Linear Scaling Method to get the Response Density Matrix in All-Electron Real-Space Density-Functional Perturbation Theory
论文作者
论文摘要
对于原子位移和均匀的电场扰动，用于响应特性的计算的真实空间密度官能扰动理论（DFPT）最近已开发并实施到全电子，数值原子原子轨道中，以数值原子为中心的轨道轨道轨道电子结构电子结构套件FHI-IAMS。发现大规模应用的瓶颈是响应密度矩阵的计算，该计算缩放为$ O（n^3）$。在这里，对于均匀电场的响应属性，我们为响应密度矩阵计算提供了有效的平行线性缩放算法。我们的方案基于二阶痕量校正纯化和平行的稀疏基质矩阵乘法算法。新方案将正式缩放量从$ O（n^3）$减少到$ O（n）$，并在数以万计的内核中显示出良好的并行可伸缩性。正如广泛验证所证明的那样，我们使用DFPT实现了准确的极化能力的快速计算。最后，通过对大规模平行的计算机系统进行缩放测试和可伸缩性测试来说明该方案的计算效率。
The real-space density-functional perturbation theory (DFPT) for the computations of the response properties with respect to the atomic displacement and homogeneous electric field perturbation has been recently developed and implemented into the all-electron, numeric atom-centered orbitals electronic structure package FHI-aims. It is found that the bottleneck for large scale applications is the computation of the response density matrix, which scales as $O(N^3)$. Here for the response properties with respect to the homogeneous electric field, we present an efficient parallel linear scaling algorithm for the response density matrix calculation. Our scheme is based on the second-order trace-correcting purification and the parallel sparse matrix-matrix multiplication algorithms. The new scheme reduces the formal scaling from $O(N^3)$ to $O(N)$, and shows good parallel scalability over tens of thousands of cores. As demonstrated by extensive validation, we achieve a rapid computation of accurate polarizabilities using DFPT. Finally, the computational efficiency of this scheme has been illustrated by making the scaling tests and scalability tests on massively parallel computer systems.
