Publications de Alfio Quarteroni

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In this work we extend to the Stokes problem the Discontinuous Galerkin Reduced Basis Element (DGRBE) method introduced in [1]. By this method we aim at reducing the computational cost for the approximation of a parametrized Stokes problem on a domain partitioned into subdomains. During an offline stage, expensive but performed only once, a low-dimensional approximation space is built on each subdomain. For any new value of the parameter, the rapid evaluation of the solution takes place during the online st

Mechanical circulatory support, in particular ventricular assist devices (VAD), has been recently proposed as an alternative to transplantation in the treatment of terminal heart failure in the context of the lack of donors and raising number of patients on the waiting list. Although these systems have proved their efficiency through a rigorous patient selection, the complication rate remains high and experience shows that many of them are related to haemodynamic modifications due to VAD implantation. Furth

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 ...

In this work we extend to the Stokes problem the Discontinuous Galerkin Reduced Basis Element (DGRBE) method introduced in Antonietti et al. (2015). By this method we aim at reducing the computational cost for the approximation of a parametrized Stokes pro ...

The purpose of the present article is to provide a theoretical analysis heterogeneous model coupling ordinary differential equations (ODEs) and partial differential equations (PDEs), providing a local-in-time existence result for the solution. The heterogeneous problem will actually be split into subproblems. The solution of the original problem will be regarded as the solution of a suitable fixed point problem, based on the successive solution of the subproblems. Moreover, the authors study the role of mat

In any sport or human endeavor, coaches regularly state “play to your strengths.” One might not guess that a land-locked, mountainous country like Switzerland would have strengths that would give them a chance at winning the oldest, most competitive sailin ...

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 ...

Since myocardial fibers drive the electric signal propagation throughout the myocardium, accurately modeling their arrangement is essential for simulating heart electrophysiology (EP). Rule-Based-Methods (RBMs) represent a commonly used strategy to include ...

In this paper we present a new approach in the study of aorto-coronaric bypass anastomoses configurations. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming branch of the bypass (the toe) into the coronary. The aim is to provide design indications in the perspective of future development for prosthetic bypasses. With a reduced model based on Stokes equations and a vorticity functional in the down field zone of bypass, a Taylor-li

In this paper we present a new reduced basis technique for parametrized nonlinear scalar conservation laws in presence of shocks. The essential ingredients are an efficient algorithm to approximate the shock curve, a procedure to detect the smooth componen ...

Background: Hemodynamics has been known to play a major role in the development of intimal hyperplasia leading to arteriovenous fistula failure. The goal of our study is to investigate the influence of different angles of side-to-end radiocephalic anastomo ...

European funding under framework 7 (FP7) for the virtual physiological human (VPH) project has been in place now for nearly 2 years. The VPH network of excellence (NoE) is helping in the development of common standards, open-source software, freely accessible data and model repositories, and various training and dissemination activities for the project. It is also helping to coordinate the many clinically targeted projects that have been funded under the FP7 calls. An initial vision for the VPH was defined

We address the coupling of an advection equation with a diffusion-advection equation, for solutions featuring boundary layers. We consider non-overlapping domain decompositions and we face up the heterogeneous problem using an extended variational formulation. We will prove the equivalence between the latter formulation and a treatment based on a singular perturbation theory. An exhaustive comparison in terms of solution and computational efficiency between these formulations is carried out.

We propose a matrix-free solver for the numerical solution of the cardiac electrophysiology model consisting of the monodomain nonlinear reaction-diffusion equation coupled with a system of ordinary differential equations for the ionic species. Our numeric ...

We propose a new, black-box online stabilization strategy for reduced basis (RB) approx- imations of parameter-dependent advection-diffusion problems in the advection-dominated case. Our goal is to stabilize the RB problem irrespectively of the stabilization (if any) op- erated on the high-fidelity (e.g. finite element) approximation, provided a set of stable RB functions have been computed. Inspired by the spectral vanishing viscosity method, our ap- proach relies on the transformation of the basis functio

We provide a computational comparison of the performance of stentless and stented aortic prostheses, in terms of aortic root displacements and internal stresses. To this aim, we consider three real patients; for each of them we draw the two prostheses configurations, which are characterized by different mechanical properties. Moreover, for each patient, we consider also the native configuration. For each scenario, we solve the fluid-structure interaction problem arising between blood and aortic root, throug

The goal of this work is the development and numerical implementation of a mathematical model describing the functioning of heart valves. To couple the pulsatile blood flow with a highly deformable thin structure (the valve's leaflets), a resistive Euleria ...

We introduce and analyze a discontinuous Galerkin method for the numerical modeling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain consi ...

Isogeometric Analysis (IGA) is used in combination with proper orthogonal decomposition (POD) for model order reduction of the time parameterized acoustic wave equations. We propose a fully discrete IGA-Newmark-POD approximation and we analyze the associated numerical error, which features three components due to spatial discretization by IGA, time discretization with the Newmark scheme, and modes truncation by POD. We prove stability and convergence. Numerical examples are presented to show the accuracy an

In this article the Stokes equations are considered in a domain simulating a capillary bed system. The capillaries are supposed to be thin, parallel and periodic. An asymptotic approximation is constructed. The macroscopic pressure satisfies a Robin interf ...

Alfio Quarteroni

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MATHICSE Technical Report : Spectral based discontinuous Galerkin reduced basis element method for parametrized Stokes problems

Connecting Ventricular Assist Devices to the Aorta: a Numerical Model

Simulation-based uncertainty quantification of human arterial network hemodynamics

Spectral based Discontinuous Galerkin Reduced Basis Element method for parametrized Stokes problems

Analysis of a geometrical multiscale model based on the coupling of ODEs and PDEs for blood flow simulations

Mathematics in the Wind

Certified Reduced Basis Approximation for Parametrized Partial Differential Equations and Applications

Modeling cardiac muscle fibers in ventricular and atrial electrophysiology simulations

Optimal control and shape optimization of aorto-coronaric bypass anastomoses

Reduced Basis Techniques For Nonlinear Conservation Laws

Computational Analysis of Turbulent Hemodynamics in Radiocephalic Arteriovenous Fistulas to Determine the Best Anastomotic Angles

A vision and strategy for the virtual physiological human in 2010 and beyond

Extended variational formulation for heterogeneous partial differential equations

A matrix-free high-order solver for the numerical solution of cardiac electrophysiology

MATHICSE Technical Report : An online intrinsic stabilization strategy for the reduced basis approximation of parametrized advection-dominated problems

MATHICSE Technical Report : aortic root stresses in presence of stentless and stented aortic valve bio-prostheses

Numerical modeling of heart valves using resistive Eulerian surfaces

Numerical modeling of the brain poromechanics by high-order discontinuous Galerkin methods

MATHICSE Technical Report : Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation

Asymptotic-numerical derivation of the Robin type coupling conditions for the macroscopic pressure at a reservoir-capillaries interface