Matrix Structure Exploitation in Generalized Eigenproblems Arising in Density Functional Theory

TL;DR

This paper introduces a new computational method to accelerate the self-consistent cycle in Density Functional Theory, specifically targeting the FLAPW implementation by exploiting matrix structures to improve eigenproblem solving efficiency.

Contribution

The paper presents a novel approach that leverages matrix structure in generalized eigenproblems to speed up DFT calculations, particularly in the FLAPW method.

Findings

Potential to significantly reduce computational time in DFT simulations

Improved efficiency in solving generalized eigenproblems

Framework adaptable to existing DFT implementations

Abstract

In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most well-known DFT implementations: FLAPW. Generating the Hamiltonian and overlap matrices and solving the associated generalized eigenproblems $Ax = \lambda Bx$ constitute the two most time-consuming fractions of each iteration. Two promising directions, implementing the new methodology, are presented that will ultimately improve the performance of the generalized eigensolver and save computational time.