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Gianluigi Rozza

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Related publications (55)

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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

Reduced basis method for parametrized elliptic optimal control problems

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Federico Negri

We propose a suitable model reduction paradigm -- the certied reduced basis method (RB) -- for the rapid and reliable solution of parametrized optimal control problems governed by partial dierential equations (PDEs). In particular, we develop the methodolo ...

Society for Industrial and Applied Mathematics2013

Reduced Basis Approximation and A Posteriori Error Estimation for the Time- Dependent Viscous Burgers Equation

Gianluigi Rozza

In this paper we present rigorous a posteriori L2 error bounds for reduced basis approximations of the unsteady viscous Burgers equation in one space dimension. The key new ingredient is accurate solution-dependent (Online) calculation of the exponential-i ...

2009

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

Gianluigi Rozza, Simone Deparis

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 Methods and A Posteriori Error Estimators for Heat Transfer Problems

Gianluigi Rozza, Simone Deparis

This paper focuses on the parametric study of steady and unsteady forced and natural convection problems by the certified reduced basis method. These problems are characterized by an input-output relationship in which given an input parameter vector — mate ...

ASME2009

Shape optimization for viscous flows by reduced basis methods and free-form deformation

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni

In this paper we further develop an approach previously introduced in [Lassila and Rozza, C.M.A.M.E 2010] for shape optimization that combines a suitable low-dimensional parametrization of the geometry (yielding a geometrical reduction) with reduced basis ...

Wiley-Blackwell2012

Comparison and combination of reduced order modelling techniques in 3D parametrized heat transfer problems

Gianluigi Rozza

Reduced Basis (RB) method has successfully been used in 2D to solve heat transfer parametrized problems. In this work, we present some 3D applications in the same field. We consider two problems, the steady Thermal Fin and the time dependent Graetz Flow, w ...

Taylor & Francis2011

A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks

Alfio Quarteroni, Gianluigi Rozza, Laura Iapichino

In this paper we propose a reduced basis hybrid method (RBHM) for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent. The RBHM is applied to Stokes equations in domains wh ...

Elsevier2012

Model reduction techniques for fast blood flow simulation in parametrized geometries

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni

In this paper we propose a new model reduction technique aimed at real-time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low-dimensional shape parametrization of the compu ...

Wiley2012

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection led and consider a stochas ...

Society for Industrial and Applied Mathematics2013

A reduced basis model with parametric coupling for fluid-structure interaction problems

Alfio Quarteroni, Gianluigi Rozza, Toni Mikael Lassila

We present a new model reduction technique for steady fluid-structure interaction problems. When the fluid domain deformation is suitably parametrized, the coupling conditions between the fluid and structure can be formulated in the low-dimensional space o ...

Society for Industrial and Applied Mathematics2012

On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition

Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at diff ...

EDP Sciences2012

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

Simulation-based uncertainty quantification of human arterial network hemodynamics

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular system based on stochastic simulation of a one dimensional arterial network. A general analysis of different uncertainties and probability characteriza ...

Wiley-Blackwell2013

Certified Reduced Basis Approximation for Parametrized Partial Differential Equations and Applications

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni

Reduction strategies, such as model order reduction (MOR) or reduced basis (RB) methods, in scientic computing may become crucial in applications of increasing complexity. In this paper we review the reduced basis method (built upon a high-delity "truth" f ...

2011

A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices

Gianluigi Rozza, Andrea Manzoni

We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...

Elsevier2013

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

An introduction to reduced basis method for parametrized PDEs

Gianluigi Rozza

We provide an introduction on reduced basis (RB) method for the solution of parameterized partial differential equations (PDEs). We introduce all the main ingredients to describe the methodology and the algorithms used to build the approximation spaces and ...

WorldScientific2009

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

Computational Reduction for Parametrized PDEs: Strategies and Applications

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni

In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...

Springer Verlag2012