Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

TL;DR

This paper discusses how mixed precision computations can improve the efficiency of eigenvalue solvers in high-performance computing projects, with detailed approaches and results in specific contexts.

Contribution

It introduces novel methods for applying mixed precision techniques to eigenvalue solvers within the ELPA-AEO and ESSEX-II projects, enhancing computational efficiency.

Findings

Mixed precision methods lead to significant efficiency gains.

Approaches are effective in multiple computational contexts.

Results demonstrate improved performance without sacrificing accuracy.

Abstract

We first briefly report on the status and recent achievements of the ELPA-AEO (Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.