Publications by Alfio Quarteroni

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In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...

This paper is an overview of known and new results about the coupling of Navier-Stokes and Darcy equations to model the filtration of incompressible fluids through porous media. We discuss coupling conditions and we analyze the global coupled model in orde ...

In this paper we describe a mathematical and numerical approach that combines physics-based simulated ground motion caused by earthquakes with fragility functions to model the structural damages induced to buildings. To simulate earthquake ground motion we ...

We present new results on the Relaxed Dimensional Factorization (RDF) preconditioner for solving saddle point problems from incompressible flow simulations, first introduced in Benzi et al. (2011). This method contains a parameter α>0α>0, to be chosen by t ...

Cardiac digital twins provide a physics and physiology informed framework to deliver personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs. Artificial Intelligence-b ...

We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison between basis functions of degree p≥1and globally Ck-continuous, with k = 0 or p − 1, to find the most accurate approximation of a propagating front with the minimal number of degrees of freedom. We show that B-spline basis functions of degree p≥1, which are Cp−1-continuous capture accurately the

We are interested in the development, implementation and testing of an orthotropic model for cardiac contraction based on an active strain decomposition. Our model addresses the coupling of a transversely isotropic mechanical description at the cell level, ...

In this paper we study the correlation between the Wall Shear Stress (WSS), a haemodynamical index derived from numerical simulations, and an new index MFA-ILT for the characterisation of intraluminal thrombus (ILT) in presence of abdominal aortic aneurysm ...

We investigate a finite element approximation of an initial boundary value problem associated with parabolic Partial Differential Equations endowed with mixed time varying boundary conditions, switching from essential to natural and vice versa. The switchi ...

We consider the numerical approximation of lipid biomembranes, including red blood cells, described through the Canham-Helfrich model, according to which the shape minimizes the bending energy under area and volume constraints. Energy minimization is performed via L2- gradient flow of the Canham-Helfrich energy using two Lagrange multipliers to weakly enforce the constraints. This yields a highly nonlinear, high order, time dependent geometric Partial Differential Equation (PDE). We represent the biomembran

In this work we introduce a new two-level preconditioner for the efficient solution of large-scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, whi ...

We developed a novel patient-specific computational model for the numerical simulation of ventricular electromechanics in patients with ischemic cardiomyopathy (ICM). This model reproduces the activity both in sinus rhythm (SR) and in ventricular tachycard ...

We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-splines or NURBS, as for example the sphere, and we spatially discretize the PDEs by means of NURBS-based Isogeometric Analysis in the framework of the standard Galerkin method. We numerically solve benchmark Laplace-Beltrami problems of the fourth and sixth o

We introduce a multiphysics and geometric multiscale computational model, suitable to describe the hemodynamics of the whole human heart, driven by a four -chamber electromechanical model. We first present a study on the calibration of the biophysically de ...

This paper presents a review of the mathematical models which can be adopted to describe the different physical phenomena characterizing the flow around a sailing yacht. The complete model accounting for laminar-turbulent transition regime, free-surface dy ...

We propose and analyse a new discontinuous reduced basis element method for the approximation of parametrized elliptic PDEs in partitioned domains. The method is built upon an offline stage (parameter independent) and an online (parameter dependent) one. I ...

In this work we address the numerical solution of large scale fluid-structure interaction problems when nonconforming grids and⁄or nonconforming finite elements discretizations are used at the interface separating the fluid and structure physical domains. ...

This work provides a review on reduced order methods in solving uncertainty quantification problems. A quick introduction of the reduced order methods, including proper orthogonal decomposition and greedy reduced basis methods, are presented along with the essential components of general greedy algorithm, a posteriori error estimation and Offline-Online decomposition. More advanced reduced order methods are then developed for solving typical uncertainty quantification problems involving pointwise evaluation

In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems wi ...

When using Newton iterations to solve nonlinear parametrized PDEs in the context of Reduced Basis (RB)methods, the assembling of the RB arrays in the online stage depends in principle on the high-fidelityapproximation. This task is even more challenging when dealing with fully nonlinear problems, for which the global Jacobian matrix has to be entirely reassembled at each Newton step. In this paper the Discrete Empirical Interpolation Method (DEIM) and its matrix version MDEIM are exploited to perform system

Alfio Quarteroni

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PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

NavierStokes/Darcy coupling: modeling, analysis and numerical approximation

Three-dimensional physics-based earthquake ground motion simulations for seismic risk assessment in densely populated urban areas

Parameter estimates for the Relaxed Dimensional Factorization preconditioner and application to hemodynamics

Whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations

MATHICSE Technical Report : Isogeometric approximation of cardiac electrophysiology models on surfaces: an accuracy study with application to the human left atrium

On some numerical aspects of an active strain model in cardiac mechanics

Analysis of morphological and haemodynamical indexes in abdominal aortic aneurysms as preliminary indicators of intraluminal thrombus deposition

Nitsche's method for parabolic Partial Differential Equations with mixed time varying boundary conditions

MATHICSE Technical Report : Biomembrane modeling with Isogeometric Analysis

Multi space reduced basis preconditioners for large-scale parametrized PDEs

Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia

MATHICSE Technical Report : Isogeometric analysis of high order partial differential equations on surfaces

An electromechanics-driven fluid dynamics model for the simulation of the whole human heart

Mathematical models and numerical simulations for the America's Cup

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

A parallel algorithm for the solution of large-scale nonconforming fluid-structure interaction problems in hemodynamics

MATHICSE Technical Report : Reduced order methods for uncertainty quantification problems

A Reduced Order Model for Domain Decompositions with Non-conforming Interfaces

MATHICSE Technical Report : A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems