Publications de Andrea Manzoni

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

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 ...

Springer/Plenum Publishers2024

Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation

Alfio Quarteroni, Andrea Manzoni

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as th ...

Wiley2023

POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

Alfio Quarteroni, Andrea Manzoni

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) ...

FRONTIERS MEDIA SA2021

Data integration for the numerical simulation of cardiac electrophysiology

Alfio Quarteroni, Luca Dede', Andrea Manzoni, Stefano Pagani

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 ...

WILEY2021

A Computational Study of the Electrophysiological Substrate in Patients Suffering From Atrial Fibrillation

Alfio Quarteroni, Andrea Manzoni

In the context of cardiac electrophysiology, we propose a novel computational approach to highlight and explain the long-debated mechanisms behind atrial fibrillation (AF) and to reliably numerically predict its induction and sustainment. A key role is pla ...

FRONTIERS MEDIA SA2021

Outer loop and isthmus in ventricular tachycardia circuits: Characteristics and implications

Alfio Quarteroni, Luca Dede', Andrea Manzoni, Stefano Pagani

BACKGROUND The isthmus of ventricular tachycardia (VT) circuits has been extensively characterized. Few data exist regarding the contribution of the outer loop (OL) to the VT circuit. OBJECTIVE The purpose of this study was to characterize the electrophysi ...

2020

Deep learning-based reduced order models in cardiac electrophysiology

Alfio Quarteroni, Luca Dede', Andrea Manzoni

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depola ...

2020

Multi space reduced basis preconditioners for parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

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 ...

PERGAMON-ELSEVIER SCIENCE LTD2019

A saddle point approach to an optimal boundary control problem for steady Navier-Stokes equations

Alfio Quarteroni, Andrea Manzoni

In this paper we propose a saddle point approach to solve boundary control problems for the steady Navier-Stokes equations with mixed Dirichlet-Neumann boundary conditions, both in two and three dimensions. We provide a comprehensive theoretical framework ...

2019

An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

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 ...

ELSEVIER SCIENCE SA2019

Hyper-reduced order models for parametrized unsteady Navier-Stokes equations on domains with variable shape

Andrea Manzoni, Niccolò Dal Santo

In this work, we set up a new, general, and computationally efficient way to tackle parametrized fluid flows modeled through unsteady Navier-Stokes equations defined on domains with variable shape, when relying on the reduced basis method. We easily descri ...

SPRINGER2019

Multi space reduced basis preconditioners for large-scale parametrized PDEs

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

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 ...

2018

An Adjoint-Based Method For The Numerical Approximation Of Shape Optimization Problems In Presence Of Fluid-Structure Interaction

Andrea Manzoni

In this work, we propose both a theoretical framework and a numerical method to tackle shape optimization problems related with fluid dynamics applications in presence of fluid-structure interactions. We present a general framework relying on the solution ...

EDP SCIENCES S A2018

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

Alfio Quarteroni, Christian Vergara, Andrea Manzoni

Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseas ...

Cambridge Univ Press2017

A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics

Alfio Quarteroni, Andrea Manzoni

When relying on Newton iterations to solve nonlinear problems in the context of Reduced Basis (RB) methods, the assembling of the RB arrays during the online stage depends on the dimension of the underlying high-fidelity approximation. This is more of an i ...

Elsevier Science Sa2017

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

Andrea Manzoni

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential ...

Iop Publishing Ltd2017

Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Elena Faggiano

A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the hemodynamics for different flow conditions occurring in n ...

Springer Heidelberg2017

A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion equations

Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

We analyze the numerical performance of a preconditioning technique recently proposed in [1] for the efficient solution of parametrized linear systems arising from the finite element (FE) discretization of parameter-dependent elliptic partial differential ...

Walter de Gruyter GmbH2017

A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem

Andrea Manzoni

In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection of small inhomoge ...

Institute of Physics2017

Reduced Basis Approximation And A Posteriori Error Estimates For Parametrized Elliptic Eigenvalue Problems

Nicola Parolini, Andrea Manzoni

We develop a new reduced basis (RB) method for the rapid and reliable approximation of parametrized elliptic eigenvalue problems. The method hinges upon dual weighted residual type a posteriori error indicators which estimate, for any value of the paramete ...

Edp Sciences S A2016