Publications by Alfio Quarteroni

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We consider the incompressible, isothermal and inertialess flow of an Oldroyd-B viscoelastic fluid in the absence of body forces. We report numerical results on the simulation of unsteady flow of an Oldroyd-B fluid by spectral element methods. Several techniques to cure the instabilities are considered

In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisso ...

In this paper we propose a new, purely algebraic, Petrov-Galerkin reduced basis (RB) method to solve the parametrized Stokes equations, where parameters serve to identify the (variable) domain geometry. Our method is obtained as an algebraic least squares reduced basis (aLS-RB) method, and improves the existing RB methods for Stokes equations in several directions. First of all, it does not require to enrich the velocity space, as often done when dealing with a velocitypressure formulation, relying on a Pet

Summary: For the simulation of two-dimensional incompressible flows, the Navier-Stokes equations can be coupled with models of reduced complexity, such as Oseen and Stokes models. This approach is briefly reviewed here. Then we propose a numerical solution of the coupled problem by subdomain splitting. We give numerical results obtained by finite element and spectral element approximations on a couple of test problems of physical interest.

Accurate reconstruction of the right heart geometry and motion from time-resolved medical images is crucial for diagnostic enhancement and computational analysis of cardiac blood dynamics. Commonly used segmentation and/or reconstruction techniques, exclus ...

We consider a Galerkin Finite Element approximation of the Stokes–Darcy problem which models the coupling between surface and groundwater flows. Then we propose an iterative subdomain method for its solution, inspired to the domain decomposition theory. The convergence analysis that we develop is based on the properties of the discrete Steklov–Poincaré operators associated to the given coupled problem. An optimal preconditioner for Krylov methods is proposed and analyzed.

We investigate the blood flow inside idealized left ventricles with prescribed wall movement by defining a formulation of boundary conditions for the Navier-Stokes equations accounting for the valves. Specifically, we consider an extended Nitsche’s method ...

We present some preliminary results on the coupling of shallow water equations for free surface flows and Darcy equation for groundwater flows. A suitable set of interface conditions is discussed: the Beavers-Joseph formula for bottom stress is used. An iterative algorithm to solve the coupled problem is proposed, and some numerical results are presented.

European funding under Framework 7 (FP7) for the virtual physiological human (VPH) project has been in place now for 5 years. The VPH Network of Excellence (NoE) has been set up to help develop common standards, open source software, freely accessible data ...

A system of differential equations for coupled fluid and drug transport in vascularized (malignant) tissues is derived by a multiscale expansion. We start from mass and momentum balance equations, stated in the physical domain, geometrically characterized ...

In this paper we address the numerical approximation of the incompressible Navier-Stokes equations in a moving domain by the spectral element method and high order time integrators. We present the Arbitrary Lagrangian Eulerian (ALE) formulation of the inco ...

We present a model for the electrophysiology in the heart to handle the electrical propagation through the Purkinje system and in the myocardium, with two-way coupling at the Purkinje-muscle junctions. In both the subproblems the monodomain model is consid ...

In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the ...

We consider a differential system based on the coupling of the Navier-Stokes and Darcy equations for modeling the interaction between surface and porous media flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) S ...

The Ã cole Polytechnique FÃ©dÃ©rale de Lausanne (EPFL) has acted as official scientific advisor for the Alinghi Team, winner of the 2003 Edition of the America's Cup. In this report we discuss the role plaid by mathematical and numerical models in yacht design. In particular, several numerical simulations based on the approximate solution of the Reynolds Averaged Navier-Stokes Equations (RANS) are addressed. Numerical results in different research areas (design of appendages, free-surface flows, aerodynamic

In a recent paper [CITE] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem.

In this paper we consider the coupling between two diffusion-reaction problems, one taking place in a three-dimensional domain Ω, the other in a one-dimensional subdomain Λ. This coupled problem is the simplest model of fluid flow in a three-dimensional po ...

Nel seguito verrà discusso il ruolo della modellistica matematica e del calcolo scientifico nelle scienze applicate, la loro rilevanza come strumenti di simulazione, indagine e supporto alle decisioni, il loro contributo all’innovazione tecnologica. Si citeranno alcuni risultati conseguiti e le prospettive che si aprono in svariati settori quali l’industria, l’ambiente, le scienze della vita e lo sport.

We investigate a one-dimensional model of blood flow in human arteries. In particular, we consider the case when an abrupt variation of mechanical characteristic of artery is caused by the presence of a vascular prosthesis. The derivations of the model and of a numerical scheme adopted for its solution are detailed. Numerical experiments show the effectiveness of the model.

In the framework of efficient partitioned numerical schemes for simulating multiphysics PDE problems, we propose using intergrid transfer operators based on radial basis functions to accurately exchange information among different PDEs defined in the same ...

Alfio Quarteroni

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On the simulation of unsteady flow of an Oldroyd-B fluid by spectral methods

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

MATHICSE Technical Report : An algebraic least squares reduced basis method for the solution of parametrized Stokes equations

Iterative solutions of multimodels for incompressible flows

Accurate Reconstruction of Right Heart Shape and Motion From Cine-MRI for Image-Driven Computational Hemodynamics

Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations

Modelling blood flows in the heart: extended Nitsche's method for the treatment of the valves as generalized boundary conditions

Coupling of free surface and groundwater flows

A vision and strategy for the virtual physiological human: 2012 update

Multiscale homogenization for fluid and drug transport in vascularized malignant tissues

High order methods for the approximation of the incompressible Navier-Stokes equations in a moving domain

A coupled 3D-1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network

On the physical consistency between three-dimensional and one-dimensional models in haemodynamics

Numerical analysis of the Navier-Stokes/Darcy coupling

Simulazione numerica per la Coppa America di vela

Multimodels for incompressible flows: iterative solutions for the Navier-Stokes/Oseen coupling

On the coupling of 1D and 3D Diffusion-Reaction Equations: Application to Tissue Pefusion Problems

Modellistica Matematica e Calcolo Scientifico

A one-dimensional model for blood flow: Application to vascular prosthesis

An intergrid transfer operator using radial basis functions with application to cardiac electromechanics