# Analytical PAW Projector Functions for Reduced Bandwidth Requirements

## TL;DR

This paper introduces an analytical basis for PAW projector functions in DFT calculations, significantly reducing memory bandwidth needs and improving scalability on high-performance computing systems, especially GPUs.

## Contribution

It proposes a 3D factorizable Hermite basis for PAW projectors and an on-the-fly sampling method to minimize memory transfer, enhancing performance in large-scale DFT computations.

## Key findings

- Reduced memory bandwidth requirements demonstrated on GPUs
- Performance improvements in projection operations
- Potential for better scalability in distributed systems

## Abstract

Large scale electronic structure calculations require modern high performance computing (HPC) resources and, as important, mature HPC applications that can make efficient use of those. Real-space grid-based applications of Density Functional Theory (DFT) using the Projector Augmented Wave method (PAW) can give the same accuracy as DFT codes relying on a plane wave basis set but exhibit an improved scalability on distributed memory machines. The projection operations of the PAW Hamiltonian are known to be the performance critical part due to their limitation by the available memory bandwidth. We investigate on the utility of a 3D factorizable basis of Hermite functions for the localized PAW projector functions which allows to reduce the bandwidth requirements for the grid representation of the projector functions in projection operations. Additional on-the-fly sampling of the 1D basis functions eliminates the memory transfer almost entirely. For an quantitative assessment of the expected memory bandwidth savings we show performance results of a first implementation on GPUs. Finally, we suggest a PAW generation scheme adjusted to the analytically given projector functions.