A Parallel and Scalable Iterative Solver for Sequences of Dense Eigenproblems Arising in FLAPW

TL;DR

This paper introduces a parallel, scalable eigensolver tailored for sequences of dense eigenproblems in FLAPW density functional theory, leveraging correlation between problems for improved efficiency.

Contribution

It presents a novel eigensolver based on subspace iteration and Chebyshev acceleration, optimized for parallel execution and sequences of correlated eigenproblems.

Findings

Achieves excellent scalability in parallel environments.

Competitive performance against existing dense eigensolvers.

Effectively exploits correlation between sequential eigenproblems.

Abstract

In one of the most important methods in Density Functional Theory - the Full-Potential Linearized Augmented Plane Wave (FLAPW) method - dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly correlated to the next one in the sequence. We propose a novel approach which exploits such correlation through the use of an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials. The resulting solver, parallelized using the Elemental library framework, achieves excellent scalability and is competitive with current dense parallel eigensolvers.