GEneral fraMework for Preconditioning and AuGmentations

Objective

This fellowship develops a general acceleration framework for the problem of the action of a function valued on an operator times a vector, whose state-of-the-art solution methods often suffer from poor convergence and scaling, limiting realistic physical system sizes. The methods developed will be used in the acceleration of the main computational bottleneck in the GW approximation, which is a powerful method in many body perturbation theory for materials simulations. In the context of the numerical linear algebra problem, I will design the first unified approach that combines polynomial and randomized preconditioning with augmentation for functions in general, and then extend it toward stationary algebraic multigrid, while demonstrating end-to-end impact by reformulating and speeding up GW self-energy calculations. The results will be released as open-source, production-grade modules first in VOTCA/XTP and then in the widely used Yambo code, with documented APIs, tests and user materials, targeting 2–4x speedups on representative benchmarks and improved scaling with the physical system size. The work directly addresses a priority need in exascale-ready electronic-structure software and supports Europe’s digital and green transitions by enabling larger, more accurate studies of semiconductors and solar-cell materials. The fellowship provides interdisciplinary training at TU/e (Netherlands) with a secondment at CNR Instituto Nanoscienze (Italy), structured two-way knowledge transfer with the beneficiary, increased uptake by the developer and user communities via the secondment, and strong open-science and outreach practices.