Publications de Tommaso Vanzan

A Performance Comparison of Classical Volume and New Substructured One- and Two-Level Schwarz Methods in PETSc

Substructured Schwarz methods are interpretations of volume Schwarz methods as algorithms on interface variables. ...

Springer Science and Business Media Deutschland GmbH2024

A multigrid method for PDE-constrained optimization with uncertain inputs

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective ...

Springer Science and Business Media LLC2024

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

Fabio Nobile, Tommaso Vanzan

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

2024

Weak Scalability of Domain Decomposition Methods for Discrete Fracture Networks

Tommaso Vanzan

Discrete Fracture Networks (DFNs) are complex three-dimensional structures characterized by the intersections of planar polygonal fractures, and are used to model flows in fractured media. Despite being suitable for Domain Decomposition (DD) techniques, th ...

Springer Science and Business Media Deutschland GmbH2024

A numerical algorithm based on probing to find optimized transmission conditions

Tommaso Vanzan

Optimized Schwarz Methods (OSMs) are based on optimized transmission conditions along the interfaces between the subdomains. Optimized transmission conditions are derived at the theoretical level, using techniques developed in the last decades. The hypothe ...

Springer-Verlag2023

Robust optimization of control parameters for WEC arrays using stochastic methods

Tommaso Vanzan, Edie Miglio

This work presents a new computational optimization framework for the robust control of parks of Wave Energy Converters (WEC) in irregular waves. The power of WEC parks is maximized with respect to the individual control damping and stiffness coefficients ...

Journal of Computational Physics2023

Preconditioners for robust optimal control problems under uncertainty

Fabio Nobile, Tommaso Vanzan

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

2023

Optimized Schwarz methods for the time-dependent Stokes-Darcy coupling

Tommaso Vanzan

This paper derives optimized coefficients for optimized Schwarz iterations for the time-dependent Stokes-Darcy problem using an innovative strategy to solve a nonstandard min-max problem. The coefficients take into account both physical and discretization ...

OXFORD UNIV PRESS2023

On the asymptotic optimality of spectral coarse spaces

Tommaso Vanzan

This paper is concerned with the asymptotic optimality of spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are known to be very ef ...

Springer-Verlag2023

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

Tommaso Vanzan

The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...

Springer-Verlag2023