An efficient GPU algorithm for tetrahedron-based Brillouin-zone integration

TL;DR

This paper introduces a GPU-optimized tetrahedron method algorithm for efficient momentum-space integrals in solid state physics, achieving significant speedups over CPU implementations, applicable to various integrals.

Contribution

The paper presents a novel GPU algorithm based on the tetrahedron method, optimized for single precision, with demonstrated high performance in calculating density of states.

Findings

Speedups of up to 130x over CPU when data transfer overheads exist.

Speedups of up to 165x over CPU when integrated into GPU programs.

Algorithm is general and applicable to various momentum integrals.

Abstract

We report an efficient algorithm for calculating momentum-space integrals in solid state systems on modern graphics processing units (GPUs). Our algorithm is based on the tetrahedron method, which we demonstrate to be ideally suited for execution in a GPU framework. In order to achieve maximum performance, all floating point operations are executed in single precision. For benchmarking our implementation within the CUDA programming framework we calculate the orbital-resolved density of states in an iron-based superconductor. However, our algorithm is general enough for the achieved improvements to carry over to the calculation of other momentum integrals such as, e.g. susceptibilities. If our program code is integrated into an existing program for the central processing unit (CPU), i.e. when data transfer overheads exist, speedups of up to a factor $\sim130$ compared to a pure CPU implementation can be achieved, largely depending on the problem size. In case our program code is integrated into an existing GPU program, speedups over a CPU implementation of up to a factor $\sim165$ are possible, even for moderately sized workloads.