Publications by Gianluigi Rozza

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

Fabio Zoccolan, Gianluigi Rozza

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

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 ...

Springer Heidelberg2016

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

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

MATHICSE Technical Report : A fast virtual surgery platform for many scenarios haemo-dynamics 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 by-pass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in ...

MATHICSE2016

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

MATHICSE Technical Report : Reduced order methods for uncertainty quantification problems

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

This work provides a review on reduced order methods in solving uncertainty quantification problems. A quick introduction of the reduced order methods, including proper orthogonal decomposition and greedy reduced basis methods, are presented along with the ...

MATHICSE2015

MATHICSE Technical Report : 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

MATHICSE2015

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