GPU-Acceleration of the ELPA2 Distributed Eigensolver for Dense Symmetric and Hermitian Eigenproblems

Abstract

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems can easily exceed the capacity of a single compute node, thus must be solved on distributed-memory parallel computers. We here present GPU-oriented optimizations of the ELPA two-stage tridiagonalization eigensolver (ELPA2). On top of cuBLAS-based GPU offloading, we add a CUDA kernel to speed up the back-transformation of eigenvectors, which can be the computationally most expensive part of the two-stage tridiagonalization algorithm. We benchmark the performance of this GPU-accelerated eigensolver on two hybrid CPU-GPU architectures, namely a compute cluster based on Intel Xeon Gold CPUs and NVIDIA Volta GPUs, and the Summit supercomputer based on IBM POWER9 CPUs and NVIDIA Volta GPUs. Consistent with previous benchmarks on CPU-only architectures, the GPU-accelerated two-stage solver exhibits a parallel performance superior to the one-stage counterpart. Finally, we demonstrate the performance of the GPU-accelerated eigensolver developed in this work for routine semi-local KS-DFT calculations comprising thousands of atoms.

References in corpus (18)

• CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations
• Quantum ESPRESSO toward the exascale
• QuantumATK: An integrated platform of electronic and atomic-scale modelling tools
• BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
• NWChem: Past, Present, and Future
• O(N) methods in electronic structure calculations
• A Density Matrix-based Algorithm for Solving Eigenvalue Problems
• Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems
• Calculations on millions of atoms with DFT: Linear scaling shows its potential
• ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers
• Large scale and linear scaling DFT with the CONQUEST code
• Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion
• What is a post-Lie algebra and why is it useful in geometric integration
• ELSI -- An Open Infrastructure for Electronic Structure Solvers
• Thermodynamic equilibrium conditions of graphene films on SiC
• GPGPU Acceleration of All-Electron Electronic Structure Theory Using Localized Numeric Atom-Centered Basis Functions
• Optimizations of the Eigensolvers in the ELPA Library
• Assessment of localized and randomized algorithms for electronic structure

Cited by in corpus (12)

• Roadmap on Electronic Structure Codes in the Exascale Era
• GPU Acceleration of Large-Scale Full-Frequency GW Calculations
• ELSI -- An Open Infrastructure for Electronic Structure Solvers
• GPGPU Acceleration of All-Electron Electronic Structure Theory Using Localized Numeric Atom-Centered Basis Functions
• Efficient All-electron Hybrid Density Functionals for Atomistic Simulations Beyond 10,000 Atoms
• Top-down fabrication of atomic patterns in twisted bilayer graphene
• Fermionic Quantum Turbulence: Pushing the Limits of High-Performance Computing
• Time-dependent nuclear energy-density functional theory toolkit for neutron star crust: Dynamics of a nucleus in a neutron superfluid
• Integrated workflows and interfaces for data-driven semi-empirical electronic structure calculations
• Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures
• Structural Anisotropy in Sb Thin Films
• GPU Acceleration of Collinear and Noncollinear DFT Using a Numerical Atomic Orbital-Based DFT Code