Sede ufficiale: LARGO BRUNO PONTECORVO, 5, 56127 PISA
Email: fabio.durastante@unipi.it
Telefono: 050 2213232
Sito web: https://fdurastante.github.io/
We promote the dissemination of knowledge and support social transformation, contributing to the progress of both the community and the region
Sede ufficiale: LARGO BRUNO PONTECORVO, 5, 56127 PISA
Email: fabio.durastante@unipi.it
Telefono: 050 2213232
Sito web: https://fdurastante.github.io/
Struttura: Dipartimento di Matematica
Settore scientifico-disciplinare: Analisi Numerica MATH-05/A
Modalità: 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).
Luogo: BBB: https://hausdorff.dm.unipi.it/b/fab-e7l-8ph-nwh Ufficio: Dipartimento di Matematica, Ufficio 107, piano terra.
Orario: Giovedì dalle 9.00 alle 10.45
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.