Fabio  Durastante Author of Evaluating Organization Development
FEATURED AUTHOR

Fabio Durastante

PhD - Research Fellow
Università di Pisa

Fabio Durastante currently works at the Department of Computer Science, Università di Pisa. Fabio does research in Parallel Computing, Algorithms and Applied Mathematics for Numerical Linear Algebra problems.

Biography

I have taken my bachelor and master degrees in Mathematics at University of Rome "Tor Vergata", then I moved to the University of Insubria (in Como, CO) for my PhD. After completion, I have started working as a Research Fellow at the University of Pisa in the Information Technology Department. I am a member of both the INDAM/GNCS and SIAM.

Areas of Research / Professional Expertise

    My main area of research is Numerical Linear Algebra. I work with preconditioned iterative methods for the solution of linear systems mostly coming from the discretization of Differential Problems or Optimization Problems. I have experiences with both technical and theoretical issues, from the implementation of algorithms in GPU framework to asymptotical spectral analysis for matrix sequences.

Websites

Books

Featured Title
 Featured Title - Iterative Methods and Preconditioning for Large and Sparse - 1st Edition book cover

Articles

Applied Numerical Mathematics 123, 43-57

Fractional PDE constrained optimization: An optimize-then-discretize approach with L-BFGS and approximate inverse preconditioning


Published: Jan 01, 2018 by Applied Numerical Mathematics 123, 43-57
Authors: Stefano Cipolla and Fabio Durastante
Subjects: Computer Science & Engineering, Mathematics

In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation. Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver.

Linear Algebra and its Applications Volume 533, 15 November 2017, Pages 507-535

Optimizing a multigrid Runge–Kutta smoother for variable-coefficient ...


Published: Nov 21, 2017 by Linear Algebra and its Applications Volume 533, 15 November 2017, Pages 507-535
Authors: Marco Donatelli and Daniele Bertaccini and Fabio Durastante and Stefano Serra Capizzano
Subjects: Computer Science & Engineering, Mathematics

The theory of Generally Locally Toeplitz (or GLT for short) sequences of matrices is proposed in the analysis of a multigrid solver for the linear systems generated by finite volume/finite difference approximations of variable-coefficients linear convection–diffusion equations in 1D and 2D problems. The multigrid solver is used with a Runge–Kutta smoother. Optimal coefficients for the smoother are found by considering the unsteady linear advection equation and using optimization algorithms.

Numerical Algorithms April 2017, Volume 74, Issue 4, pp 1061–1082

Solving mixed classical and fractional partial differential equations using ...


Published: Apr 30, 2017 by Numerical Algorithms April 2017, Volume 74, Issue 4, pp 1061–1082
Authors: Daniele Bertaccini and Fabio Durastante
Subjects: Computer Science & Engineering, Mathematics

The efficient numerical solution of the large linear systems of fractional differential equations is considered here. The key tool used is the short–memory principle. The latter ensures the decay of the entries of the inverse of the discretized operator, whose inverses are approximated here by a sequence of sparse matrices. On this ground, we propose to solve the underlying linear systems by iterative solvers using sequence of preconditioners based on the above mentioned inverses.

Computers & Mathematics with Applications 72.4

Interpolating preconditioners for the solution of sequence of linear systems


Published: Aug 31, 2016 by Computers & Mathematics with Applications 72.4
Authors: Daniele Bertaccini and Fabio Durastante
Subjects: Computer Science & Engineering, Mathematics

A new strategy for updating preconditioners by polynomial interpolation of factors of approximate inverse factorizations is proposed here. The computational cost per iteration is linear in the number of degree of freedom, the same order of most of the strategies for updating an incomplete factorization proposed in the last decade. The effectiveness of the technique is confirmed by some experiments.