Mohr Stephan, Dawson William, Wagner Michael, Caliste Damien, Nakajima Takahito, Genovese Luigi
Barcelona Supercomputing Center (BSC) , 08034 Barcelona, Spain.
RIKEN Advanced Institute for Computational Science , Kobe 650-0002, Japan.
J Chem Theory Comput. 2017 Oct 10;13(10):4684-4698. doi: 10.1021/acs.jctc.7b00348. Epub 2017 Sep 27.
We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.
我们展示了CheSS，即“切比雪夫稀疏求解器”库，它旨在解决使用局域基组进行大规模电子结构计算时出现的典型问题。该库基于切比雪夫多项式的灵活高效展开，目前具有密度矩阵计算、任意幂次的矩阵幂计算以及在选定区间内提取特征值的功能。CheSS能够利用矩阵的稀疏性，并且相对于非零元素的数量呈线性扩展，使其非常适合大规模计算。该方法特别适用于导致所涉及矩阵的谱宽较小的设置，并且在这种情况下优于其他方法。通过将CheSS与DFT代码BigDFT耦合，我们表明这种有利的设置在实际中确实可行。此外，基于切比雪夫多项式的方法可以大规模并行化，并且即使对于相对较小的矩阵规模，CheSS在扩展到数千个核心时也表现出出色的性能。
