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Gianluigi Rozza

Cette personne a quitté l’EPFL

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Publications associées (55)

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Real-Time Reliable Simulation of Heat Transfer Phenomena

Gianluigi Rozza

In this paper we discuss the application of the certified reduced basis method and the associated software package rbMIT (c) to ``worked problems'' in steady and unsteady conduction. Each worked problem is characterized by an input parameter vector --- mat ...

ASME2009

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

Stabilized reduced basis method for parametrized advection-diffusion PDEs

Gianluigi Rozza, Paolo Pacciarini

In this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Onl ...

Elsevier2014

Real-time reduced basis solutions for Navier-Stokes equations: optimization of parametrized bypass configurations

Gianluigi Rozza

The reduced basis method on parametrized domains is applied to approximate blood flow through an arterial bypass. The aim is to provide (a) a sensitivity analysis for relevant geometrical quantities of interest in bypass configurations and (b) rapid and re ...

2006

Model reduction of semiaffinely parameterized partial differential equations by two-level affine approximation

Gianluigi Rozza, Toni Mikael Lassila

We propose an improvement to the reduced basis method for parametric partial differential equations. An assumption of affine parameterization leads to an efficient offline-online decomposition when the problem is solved for many different parametric config ...

2011

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

Siam Publications2013

Shape design in aorto-coronaric bypass anastomoses using perturbation theory

Alfio Quarteroni, Gianluigi Rozza

We present a new approach in the study of aorto-coronaric bypass anastomoses configurations based on small perturbation theory. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming ...

2006

Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map

Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

Reduced basis approximations for geometrically parametrized advection- diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized ...

Springer2010

Reduced basis methods for optimal control of advection-diffusion problems

Alfio Quarteroni, Gianluigi Rozza

RAS and University of Houston2007

Computing upper and lower bounds for linear outputs of elasticity by the smoothed finite element method

Alfio Quarteroni, Gianluigi Rozza, Toni Mikael Lassila

Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design for safety. In this ...

Wiley2010

A mathematical approach in the design of arterial bypass using unsteady Stokes equations

Alfio Quarteroni, Gianluigi Rozza

In this paper we present an approach for the study of aorto-coronaric bypass anastomoses configurations using unsteady Stokes equations. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the ...

2006

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

Reduction strategies for PDE-constrained optimization problems in haemodynamics

Gianluigi Rozza, Andrea Manzoni, Federico Negri

Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numeri ...

Vienna Technical University2012

Real time reduced basis techniques for arterial bypass geometries

Gianluigi Rozza

Elsevier2005

Matematica in volo con Solar Impulse

Alfio Quarteroni, Gianluigi Rozza, Nicola Parolini, Gilles Fourestey

2006