Large scale ab initio calculations based on three levels of parallelization

TL;DR

This paper introduces a novel three-level parallelization scheme for ab initio plane-wave calculations in ABINIT, significantly improving scalability and efficiency through innovative data partitioning and optimized eigenvalue solving.

Contribution

It develops a three-level parallelization approach combining k-points, bands, and Fourier space partitioning, enhancing performance and scalability of ab initio calculations.

Findings

Super-linear scaling up to 100 processors for a single k-point

Good performance up to 200 processors

Linear scaling up to 1000 processors with multiple k-points

Abstract

We suggest and implement a parallelization scheme based on an efficient multiband eigenvalue solver, called the locally optimal block preconditioned conjugate gradient LOBPCG method, and using an optimized three-dimensional (3D) fast Fourier transform (FFT) in the ab initio}plane-wave code ABINIT. In addition to the standard data partitioning over processors corresponding to different k-points, we introduce data partitioning with respect to blocks of bands as well as spatial partitioning in the Fourier space of coefficients over the plane waves basis set used in ABINIT. This k-points-multiband-FFT parallelization avoids any collective communications on the whole set of processors relying instead on one-dimensional communications only. For a single k-point, super-linear scaling is achieved for up to 100 processors due to an extensive use of hardware optimized BLAS, LAPACK, and SCALAPACK routines, mainly in the LOBPCG routine. We observe good performance up to 200 processors. With 10 k-points our three-way data partitioning results in linear scaling up to 1000 processors for a practical system used for testing.