Massively parallel implementation of iterative eigensolvers in large-scale plane-wave density functional theory

Abstract

The Kohn-sham density functional theory (DFT) is a powerful method to describe the electronic structures of molecules and solids in condensed matter physics, computational chemistry and materials science. However, large and accurate DFT calculations within plane waves process a cubic-scaling computational complexity, which is usually limited by expensive computation and communication costs. The rapid development of high performance computing (HPC) on leadership supercomputers brings new opportunities for developing plane-wave DFT calculations for large-scale systems. Here, we implement parallel iterative eigensolvers in large-scale plane-wave DFT calculations, including Davidson, locally optimal block preconditioned conjugate gradient (LOBPCG), projected preconditioned conjugate gradient (PPCG) and the Chebyshev subspace iteration (CheFSI) algorithms, and analyze the performance of these algorithms in massively parallel plane-wave computing tasks. We adopt a two-level parallelization strategy that combines the message passing interface (MPI) with open multi-processing (OpenMP) parallel programming to handle data exchange and matrix operations in the construction and diagonalization of large-scale Hamiltonian matrix within plane waves. Numerical results illustrate that these iterative eigensolvers can scale up to 42,592 processing cores with high peak performance of 30% on leadship supercomputers to study the electronic structures of bulk silicon systems containing 10,648 atoms. Program summaryProgram Title: Plane wave density functional theory (PWDFT)CPC Library link to program files:https://doi.org/10.17632/c8v2mx5vn4.1Developer's repository link:https://bitbucket.org/berkeleylab/scalesLicensing provisions: BSD 3-clauseProgramming language: C++Nature of problem: PWDFT is used for electronic structure calculations based on Kohn-Sham density functional theory. The key challenge to address is a constrained energy minimization problem, which can also be formulated as a nonlinear eigenvalue problem. MPI/OpenMP-based approaches are employed to provide multi-core acceleration for the study of the chemical and material properties of larger-scale molecules and solids.Solution method: PWDFT implements self-consistent field (SCF) iterations and direct constrained minimization algorithms with various acceleration strategies. It is written in C++ and offers parallel acceleration based on MPI/OpenMP.