Fabio Durastante

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Mode of office hours: Il ricevimento è disponibile sulla piattaforma online BBB oppure in presenza in ufficio. Inviare una mail all'indirizzo istituzionale per prenotarsi (disponibili anche altri orari).

Location: BBB: https://hausdorff.dm.unipi.it/b/fab-e7l-8ph-nwh Ufficio: Dipartimento di Matematica, Ufficio 107, piano terra.

Time: Giovedì dalle 9.00 alle 10.45

Research interests

My research centers on the efficient numerical solution of extremely large, sparse linear systems—matrices so vast that they can contain billions or even trillions of unknowns, yet sparse enough to admit specialized iterative algorithms. I develop and analyze Krylov subspace methods alongside algebraic and geometric multigrid preconditioners that adapt dynamically to sequences of related problems, achieving robust convergence at scales previously out of reach. Translating these advances into practice, I have architected high-performance software toolkits that exploit CPU and GPU parallelism—demonstrating, for instance, how cutting-edge coarsening strategies and polynomial smoothers can accelerate industrial-scale fluid dynamics codes on the world’s leading supercomputers.
Extending beyond classic linear systems, I investigate matrix functions and rational Krylov techniques, which enable the rapid evaluation of fractional powers, exponentials, and other transformations of large matrices. By leveraging low-rank corrections to update existing factorizations, these methods open new possibilities in time-dependent simulations, control applications, and network dynamics. In parallel, I explore the numerical treatment of fractional differential equations—modeling nonlocal, memory-dependent processes—by designing adaptive discretizations for Caputo-type derivatives, short-memory approximations, and specialized preconditioners that keep anomalous diffusion and wave-propagation simulations both accurate and tractable.
My interests also span matrix-theoretic approaches to complex networks and optimal control of PDEs. I have introduced walk-based centrality measures grounded in Mittag-Leffler functions to capture nuanced connectivity patterns, and I have studied nonlocal diffusion on graphs through fractional Laplacians of variable order. In the realm of PDE-constrained optimization, I analyze the spectral structure of saddle-point systems and devise optimize-then-discretize schemes—combining quasi-Newton solvers like L-BFGS with bespoke preconditioners—to tackle inverse problems and design challenges in engineering. Throughout all these endeavors, I prioritize clean, modular code—written in Fortran, C, Python, and MATLAB—and leverage MPI, OpenMP, and CUDA to ensure that theory, software, and real-world applications converge seamlessly at the exascale.
 

Publications

• Modeling advection on distance-weighted directed networks (Benzi, Michele; Durastante, Fabio; Zigliotto, Francesco - 2025 - 1.1 Articolo in rivista)
• Efficient computation of the sinc matrix function for the integration of second-order differential equations (Aceto, L.; Durastante, F. - 2024 - 1.1 Articolo in rivista)
• Theoretical error estimates for computing the matrix logarithm by Padé-type approximants (Aceto, L.; Durastante, F. - 2024 - 1.1 Articolo in rivista)
• On Kemeny's constant and stochastic complement (Bini Dario, Andrea.; Durastante, F.; Kim, Sooyeong; Meini, Beatrice - 2024 - 1.1 Articolo in rivista)
• Stochastic [{p}]th Root Approximation of a Stochastic Matrix: A Riemannian Optimization Approach (Durastante, Fabio; Meini, Beatrice - 2024 - 1.1 Articolo in rivista)
• Alya toward exascale: algorithmic scalability using PSCToolkit (Owen, H.; Lehmkuhl, O.; D'Ambra, P.; Durastante, F.; Filippone, S. - 2024 - 1.1 Articolo in rivista)
• Nocturnal Seafaring: the Reduction of Visibility at Night and its Impact on Ancient Mediterranean Seafaring. A Study Based on 8–4th Centuries BC Evidence (Mauro, C. M.; Durastante, F. - 2024 - 1.1 Articolo in rivista)
• Why diffusion-based preconditioning of Richards equation works: Spectral analysis and computational experiments at very large scale (Bertaccini, D.; D'Ambra, P.; Durastante, F.; Filippone, S. - 2023 - 1.1 Articolo in rivista)
• Automatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregations (D'Ambra, P.; Durastante, F.; Filippone, S.; Zikatanov, L. - 2023 - 1.1 Articolo in rivista)
• AMG Preconditioners based on Parallel Hybrid Coarsening and Multi-objective Graph Matching (D'Ambra, P.; Durastante, F.; Ferdous, S. M.; Filippone, S.; Halappanavar, M.; Pothen, A. - 2023 - 4.1 Contributo in Atti di convegno)

All publications by Fabio Durastante on ARPI, the Research Archive of the University of Pisa