GPU-acceleration of the ELPA2 distributed eigensolver for dense symmetric and hermitian eigenproblems

0539376 - MÚ 2022 RIV NL eng J - Journal Article
Yu, V. W. z. - Moussa, J. - Kůs, Pavel - Marek, A. - Messmer, P. - Yoon, M. - Lederer, H. - Blum, V.
GPU-acceleration of the ELPA2 distributed eigensolver for dense symmetric and hermitian eigenproblems.
Computer Physics Communications. Roč. 262, May (2021), č. článku 107808. ISSN 0010-4655. E-ISSN 1879-2944
Institutional support: RVO:67985840
Keywords : CUDA * dense linear algebra * eigensolver * high-performance computing * parallel computing
OECD category: Pure mathematics
Impact factor: 4.717, year: 2021
Method of publishing: Limited access
https://doi.org/10.1016/j.cpc.2020.107808

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.
Permanent Link: http://hdl.handle.net/11104/0317067