Publications by Alfio Quarteroni

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Scientific Machine Learning (SciML) is a recently emerged research field which combines physics-based and data-driven models for the numerical approximation of differential problems. Physics-based models rely on the physical understanding of the problem at ...

Purpose: Connecting outflow cannula of LVAD to the aorta is an underexplored issue but may have considerable impact. In fact the hemodynamic modifications due to implantation in this region can cause thromboembolic events. It is therefore important to understand the flow pattern in this region and the way device interacts with the cardiovascular system. We present here the mathematical settings and results of a numerical model of the anastomosis between the outflow cannula of LVAD and the aorta. Methods: Th

The main goal of this work is to devise robust iterative strategies to partition the solution of the Navier-Stokes equations in a three-dimensional (3D) domain, into non overlapping 3D subdomains, which communicate through the exchange of averaged/integrat ...

The cardiac Purkinje fibres provide an important stimulus to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems on the Purkinje network that is efficient enough to be used on realistic networks with physiologically detailed membrane models. The algorithm is based on operator splitting and is provided with three different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work based on the model of Vigmond e

The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this computational burden, and are nowadays exploited to accelerate real-time analysis, as well as the solution of PDE-constrained optimization and inverse problems. These methods are built upon low-dimensional spaces obtained by selecting a set of snap- shots from

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, fin

A key component in developing atrial digital twins (ADT) - virtual representations of patients’ atria — is the accurate prescription of myocardial fibers which are essential for the tissue characterization. Due to the difficulty of reconstructing atrial fi ...

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the ...

We investigate a general approach for the numerical approximation of incompressible Navier-Stokes equations based on splitting the original problem into successive subproblems which are cheaper to solve. The splitting is obtained through an algebraic approximate factorization of the matrix arising from space and time discretization of the original equations. Several schemes based on approximate factorization are investigated. For some of these methods a formal analogy with well known time advancing schemes,

This paper is concerned with the mathematical analysis of a coupled elliptic–parabolic system modeling the interaction between the propagation of electric potential and subsequent deformation of the cardiac tissue. The problem consists in a reaction–diffus ...

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 ...

We consider the numerical approximation of lipid biomembranes at equilibrium described by the Canham-Helfrich model, according to which the bending energy is minimized under area and volume constraints. Energy minimization is performed via L-2-gradient flo ...

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 ...

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...

This paper presents an analysis of hyperelastic constitutive models for continuous bodies both from a modeling and numerical point of view. Contributions are made within the context of finite element numerical simulations. Numerical results with relevance ...

Mathematical modeling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a compl ...

In this paper, we are interested in the spatio-temporal dynamics of the transmembrane potential in paced isotropic and anisotropic cardiac tissues. In particular, we observe a specific precursor of cardiac arrhythmias that is the presence of alternans in t ...

Parametrized systems of Differential Algebraic Equations (DAEs) stand at the base of several mathematical models in Microelectronics, Computational Fluid Dynamics and other Engineering fields. Since the dimension of these systems can be huge, high computat ...

In this article we address the numerical simulation of fluid-structure interaction (FSI) problems featuring large added-mass effect. We analyze different preconditioners for the coupled system matrix obtained after space- time discretization and linearizat ...

Alfio Quarteroni

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Combining physics-based and data-driven models: advancing the frontiers of research with scientific machine learning

Numerical Fluid-Structure Interaction Model for the Connection of Outflow Cannula of LVAD to the Aorta

Algorithms for the partitioned solution of weakly coupled fluid models for cardiovascular flows

MATHICSE Technical Report : Improved hybrid/GPU algorithm for solving cardiac electro-physiology problems on Purkinje networks

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Numerical Models for Differential Problems

Defining myocardial fiber bundle architecture in atrial digital twins

An active strain electromechanical model for cardiac tissue

Factorization methods for the numerical approximation of Navier-Stokes equations

Solvability analysis and numerical approximation of linearized cardiac electromechanics

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

Biomembrane modeling with isogeometric analysis

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

Multi space reduced basis preconditioners for parametrized Stokes equations

A numerical study of isotropic and anisotropic constitutive models with relevance to healthy and unhealthy cerebral arterial tissues

Integrated Heart-Coupling multiscale and multiphysics models for the simulation of the cardiac function

Finite element and finite volume-element simulation of pseudo-ECGs and cardiac alternans

Reduced Basis Method for Parametrized Differential Algebraic Equations

Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect