Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library

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.We gratefully acknowledge the support of the MaX (SM) and POP (MW) projects, which have received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 676598 and 676553, respectively. This work was also supported by the Energy oriented Centre of Excellence (EoCoE), grant agreement number 676629, funded within the Horizon2020 framework of the European Union, as well as by the Next-Generation Supercomputer project (the K computer project) and the FLAGSHIP2020 within the priority study5 (Development of new fundamental technologies for high-efficiency energy creation, conversion/storage and use) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. We (LG, DC, WD, TN) gratefully acknowledge the joint CEA-RIKEN collaboration action.Peer Reviewe