A Unified Software Interface to Solve or Circumvent the Kohn-Sham Eigenvalue Problem: ELSI

Solving or circumventing a generalized eigenvalue problem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory (KS-DFT). This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to simplify the access to existing strategies to address the KS eigenvalue problem. Supported algorithms include the massively parallel dense eigensolver ELPA ($O(N^3)$), the orbital minimization method in libOMM ($O(N^3)$ with a reduced prefactor), and the Pole EXpansion and Selected Inversion (PEXSI) approach with lower computational complexity (at most $O(N^2)$). The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by a) optional automatic selection of the correct solver depending on the specific problem; b) reasonable default parameters for a chosen solver; and c) automatic conversion between input and internal working matrix formats. Benchmarks are shown for all-electron Hamilton and overlap matrices for system sizes up to several thousand atoms. This work is supported by the National Science Foundation under Grant Number 1450280.