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Gianluigi Rozza

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Publications associées (55)

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

A reduced-order strategy for solving inverse Bayesian shape identication problems in physiological flows

Alfio Quarteroni, Gianluigi Rozza, Toni Mikael Lassila, Andrea Manzoni

A reduced-order strategy based on the reduced basis (RB) method is developed for the efficient numerical solution of statistical inverse problems governed by PDEs in domains of varying shape. Usual discretization techniques are infeasible in this context, ...

Springer2013

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

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

Gianluigi Rozza, Toni Mikael Lassila, Andrea Manzoni

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

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

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

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

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

Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization

Alfio Quarteroni, Nicola Parolini, Gianluigi Rozza, Matteo Lombardi

The numerical simulation of free-surface flows around sailing boats is a complex topic that addresses multiple mathematical tasks: the correct study of the flow field around a rigid hull, the numerical simulation of the hull dynamics, the deformation of th ...

Springer2012

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

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

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

Reduced basis approximation and error bounds for potential flows in parametrized geometries

Gianluigi Rozza

In this paper we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries. We review the essential ingredients: i) a Galerkin projection onto a low dimensional s ...

2011

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

Gianluigi Rozza, Fabrizio Gelsomino

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

Parametric free-form shape design with PDE models and reduced basis method

Gianluigi Rozza, Toni Mikael Lassila

We present a coupling of the reduced basis methods and free-form deformations for shape optimization and design of systems modelled by elliptic PDEs. The free-form deformations give a parameterization of the shape that is independent of the mesh, the initi ...

Elsevier2010

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

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

Gianluigi Rozza, Toni Mikael Lassila, Andrea Manzoni

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 and A Posteriori Error Estimators for Heat Transfer Problems

Simone Deparis, Gianluigi Rozza

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

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

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

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