Publications by Alfio Quarteroni

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In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed di ...

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 ...

We propose in this paper an Eulerian finite element approximation of a coupled chemical fluid-structure interaction problem arising in the study of mesoscopic cardiac biomechanics. We simulate the active response of a myocardial cell (here considered as an ...

Mathematical models, along with scientific theory and practical experiments, are a crucial part of modern engineering and science. The author takes a look at the role mathematical models play in topics ranging from vascular simulation to weather forecastin ...

The efficient solution of coupled PDEs/ODEs problems arising in cardiac electrophysiology is of key importance whenever interested to study the electrical behavior of the tissue for several instances of relevant physical and/or geometrical parameters. This poses significant challenges to reduced order modeling (ROM) techniques – such as the reduced basis method – traditionally employed when dealing with the repeated solution of parameter dependent differential equations. Indeed, the nonlinear nature of the

One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domain discretizations employed. Moreover, very often complex submodels depend on (e ...

We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. ...

We are interested in the numerical solution of the unsteady Navier-Stokes equations on large scale parallel architectures. We consider efficient preconditioners, such as the Pressure Convection-Diffusion (PCD), the Yosida preconditioner, the SIMPLE precond ...

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −laplace(u) = f in the domain

\Omega = (-1, 1)^d

(d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of bothcondi ...

In this paper, we investigate the haemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompres ...

Bicuspid aortic valve (BAV) is associated with aortic dilatation and aneurysm. Several studies evidenced an eccentric systolic flow in ascending aorta associated with increased wall shear stresses (WSS) and the occurrence of an helical systolic flow. This ...

We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitate ...

Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material o

This contribution addresses the mathematical modeling and numerical approximation of the excitation-contraction coupling mechanisms in the heart. The main physiological issues are preliminarily sketched along with an extended overview to the relevant literature. Then we focus on the existing models for the electromechanical interaction, paying special attention to the active strain formulation that provides the link between mechanical response and electrophysiology. We further provide some critical insight

The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implem

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 ...

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing thera ...

Interface controls are unknown functions used as Dirichlet or Robin boundary data on the interfaces of an overlapping decomposition designed for solving second order elliptic boundary value problems. The controls are computed through an optimal control pro ...

Orbitally shaken bioreactors are an emerging alternative to stirred-tank bioreactors for large-scale mammalian cell culture, but their fluid dynamics is still not well defined. Among the theoretical and practical issues that remain to be resolved, the char ...

In this paper, we present a mathematical model capable of simulating the human cardiac function. We review the basic equations of the model, their coupling, the numerical approach for the computer solution of this mathematical model, and a few examples of ...

Alfio Quarteroni

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Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

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

Fully Eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells

Mathematicals Models in Science and Engineering

MATHICSE Technical Report : Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method

Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces

Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

Parallel preconditioners for the unsteady Navier-Stokes equations and applications to hemodynamics simulations

Finite-element preconditioning of G-NI spectral methods

Hemodynamics of the heart's left atrium based on a Variational Multiscale-LES numerical method

Helical flows and asymmetry of blood jet in dilated ascending aorta with normally functioning bicuspid valve

Isogeometric Analysis for second order Partial Differential Equations on surfaces

Spectral Methods

Activation models for the numerical simulation of cardiac electromechanical interactions

Free form deformation techniques applied to 3D shape optimization problems

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

Data integration for the numerical simulation of cardiac electrophysiology

The Interface Control Domain Decomposition (Icdd) Method For Elliptic Problems

Numerical simulation of orbitally shaken viscous fluids with free surface

A mathematical model of the human heart suitable to address clinical problems