Publications by Gianluigi Rozza

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Flow simulations in pipelined channels and several kinds of parametrized configurations have a growing interest in many life sciences and industrial applications. Applications may be found in the analysis of the blood flow in specific compartments of the c ...

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 ...

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 ...

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) ...

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 ...

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 ...

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 ...

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities – which are mainly related either to nonlin ...

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 ...

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 ...

We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid-structure interaction problems and the management of structural deformations, namely, to represen ...

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 ...

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, ...

We extend the classical empirical interpolation method to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori c ...

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 ...

In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in affinely parametrized geometries, focusing on the role played by the Brezzi's and Babuska's stability constants. The crucial ...

The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper we apply a domain parametrization technique to reduce both the geometrical and computational complexity of the forward problem, and replace the finit ...

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 ...

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 ...

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 ...

Gianluigi Rozza

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Reduced basis method for the Stokes equations in decomposable parametrized domains using greedy optimization

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

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

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

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

Reduced basis method for linear elasticity problems with many parameters

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

Model order reduction in fluid dynamics: challenges and perspectives

Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization

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

Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid-structure interaction coupling problems

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

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

A weighted empirical interpolation method: a priori convergence analysis and applications

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants

A reduced computational and geometrical framework for inverse problems in haemodynamics

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

Reduced basis method for parametrized elliptic optimal control problems

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