Publications by Gianluigi Rozza

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Walter De Gruyter Gmbh2024

Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Elena Faggiano

A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the hemodynamics for different flow conditions occurring in n ...

Springer Heidelberg2017

Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain ...

Springer2016

Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Elena Faggiano

In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algor ...

Elsevier2016

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Alfio Quarteroni, Gianluigi Rozza, Laura Iapichino

The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to ...

Elsevier2016

Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni

In this work we present a stable proper orthogonal decomposition (POD)-Galerkin approximation for parametrized steady incompressible Navier-Stokes equations with low Reynolds number. Supremizers solutions are added to the reduced velocity space in order to ...

Wiley-Blackwell2015

Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations

Gianluigi Rozza, Andrea Manzoni, Federico Negri

This paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties ...

Elsevier2015

Comparison between reduced basis and stochastic collocation methods for elliptic problems

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

The stochastic collocation method has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method, primarily developed for solving parametric systems, has been recently used to deal with ...

Springer Verlag2014

Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid-structure interaction coupling problems

Gianluigi Rozza, Davide Forti

We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid-structure interaction problems and the management of structural deformations, namely, to represen ...

Taylor & Francis2014

A weighted empirical interpolation method: a priori convergence analysis and applications

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

We extend the classical empirical interpolation method to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori c ...

EDP Sciences2014