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Gianluigi Rozza

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Publications associées (55)

Reduced basis methods for Stokes equations in domains with non-affine parameter dependence

Gianluigi Rozza

In this paper we deal with reduced basis techniques applied to Stokes equations. We consider domains with different shape, parametrized by affine and non-affine maps with respect to a reference domain. The proposed method is ideally suited for the repeated ...

Springer-Verlag2009

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

Reduced basis method for multi-parameter dependent steady Navier-Stokes equations: applications to natural convection in a cavity

Simone Deparis, Gianluigi Rozza

This work focuses on the approximation of parametric steady Navier-- Stokes equations by the reduced basis method. For a particular instance of the parameters under consideration, we are able to solve the underlying partial differential equations, compute ...

2009

Reduced basis method for linear elasticity problems with many parameters

Alfio Quarteroni, Gianluigi Rozza

he reduced basis (RB) methods are proposed here for the solution of parametrized equations in linear elasticity problems. The fundamental idea underlying RB methods is to decouple the generation and projection stages (offline/online computational procedure ...

2008

Numerical solution of parametrized Navier-Stokes equations by reduced basis methods

Alfio Quarteroni, Gianluigi Rozza

We apply the reduced basis method to solve Navier-Stokes equations in parametrized domains. Special attention is devoted to the treatment of the parametrized nonlinear transport term in the reduced basis framework, including the case of nonaffine parametri ...

2007

Reduced basis methods for optimal control of advection-diffusion problems

Alfio Quarteroni, Gianluigi Rozza, Annalisa Quaini

RAS and University of Houston2007

On the stability of Reduced Basis methods for Stokes Equations in parametrized domains

Gianluigi Rozza

We present an application of reduced basis method for Stokes equations in domains with affine parametric dependence. The essential components of the method are (i) the rapid convergence of global reduced basis approximations – Galerkin projection onto a sp ...

2007

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

Matematica in volo con Solar Impulse

Alfio Quarteroni, Nicola Parolini, Gianluigi Rozza, Gilles Fourestey

2006

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

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

Real time reduced basis techniques for arterial bypass geometries

Gianluigi Rozza

Elsevier2005

On optimization, control and shape design of an arterial bypass

Gianluigi Rozza

Multi-level geometrical approaches in the study of aorto-coronaric bypass anastomoses configurations are discussed. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the incoming branch of the bypass (t ...

2005

Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity

Gianluigi Rozza

We present an application in multi-parametrized sub-domains based on a technique for the rapid and reliable prediction of linear-functional outputs of elliptic coercive partial differential equations with affine parameter dependence (reduced-basis methods) ...

2005

Shape design by optimal flow control and reduced basis techniques : applications to bypass configurations in haemodynamics

Gianluigi Rozza

The purpose of this thesis is to develop numerical methods for optimization, control and shape design in computational fluid dynamics, more precisely in haemodynamics. The application studied is related with the shape optimization of an aorto-coronaric byp ...

EPFL2005

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