Publications by Simone Deparis

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As Saitta et al. report in [1], the flipped classroom model builds on several well-known teaching approaches. In particular, using in-class time for more active learning activities as been constantly shown by research to improve learning [2]. In this presentation, we report about a pilot class in Linear Algebra for Engineers at EPFL that has implemented the flipped classroom model during two years. To allow for an analysis of the performances of the students, the course has implemented three features. First

We consider a fluid–structure interaction (FSI) problem discretized by finite elements featuring two different grids that do not necessarily agree on the interface separating the computational domain of the fluid from the one of the structure. After identifying a master domain (the structural domain) and a slave domain (the fluid domain), we build up two radial basis function (RBF) inter-grid operators, one Π_fs from master to slave, and the other Π_sf from slave to master. Then, we enforce the kinematic co

Simulating arterial trees in the cardiovascular system can be made by the help of different models, depending on the outputs of interest and the desired degree of accuracy. In particular, one-dimensional fluid-structure interaction models for arteries are ...

We consider a fluid-structure interaction (FSI) problem discretized by finite elements featuring two different grids that do not necessarily agree on the interface separating the computational domain of the fluid from the one of the structure. After identifying a master domain (the structural domain) and a slave domain (the fluid domain), we build up two Radial Basis Function (RBF) inter-grid operators, one Pfs from master to slave, and the other Psf from slave to master. Then, we enforce the kinematic cond

This work is focused on the development of a geometrical multiscale framework for modeling the human cardiovascular system. This approach is designed to deal with different geometrical and mathematical models at the same time, without any preliminary hypotheses on the layout of the general multiscale problem. This flexibility allows to set up a complete arterial tree model of the circulatory system, assembling first a network of one-dimensional models, described by non-linear hyperbolic equations, and then

We analyze the numerical performance of a preconditioning technique recently proposed in [4] for the ecient solution of parametrized linear systems arising from the finite element (FE) discretization of parameter-dependent elliptic partial differential equations (PDEs). In order to exploit the parametric dependence of the PDE, the proposed preconditioner takes advantage of the reduced basis (RB) method within the preconditioned iterative solver employed to solve the linear system, and combines a RB solver,

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 ...

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 ...

This work focuses on the approximation of parametric steady Navier-- Stokes equations by the reduced basis method. For a particular instance of the parameters under consideration, we are able to solve the underlying partial differential equations, compute ...

Domain-decomposition (DD) methods are used in most, if not all, modern parallel implementations of finite element modeling software. In the solver stage, the algebraic additive Schwarz (AAS) domain-decomposition preconditioner represents a fundamental comp ...

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 ...

From basic science to translation, modern biomedical research demands computational models which integrate several interacting physical systems. This paper describes the infrastructural framework for generic multiphysics integration implemented in the soft ...

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 ...

This paper focuses on the parametric study of steady and unsteady forced and natural convection problems by the certified reduced basis method. These problems are characterized by an input-output relationship in which given an input parameter vector — mate ...

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. ...

Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local PDE and some aver ...

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 ...

This work focuses on the development of a non-conforming method for the coupling of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a finite number of Lagrange multipliers defined over the interfac ...

In this work we introduce a two-level preconditioner for the efficient solution of large scale saddlepoint linear systems arising from the finite element (FE) discretization of parametrized Stokes equations.The proposed preconditioner extends the Multi Space Reduced Basis (MSRB) preconditioning methodproposed in [12], and relies on the combination of an approximated block (fine grid) preconditioner witha reduced basis solver, which plays the role of coarse component. A sequence of RB spaces, constructedeith

The numerical tools to simulate blood flow in the cardiovascular system are constantly developing due to the great clinical interest and to scientific advances in mathematical models and computational power. The present work aims to address and validate ne ...

Simone Deparis

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Flipped classroom in Linear Algebra

A Fluid–Structure Interaction Algorithm Using Radial Basis Function Interpolation Between Non-Conforming Interfaces

Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels

MATHICSE Technical Report : A fluid-structure interaction algorithm using radial basis function interpolation between non-conforming interfaces

Algorithms for the coupling of one-dimensional arterial networks with three-dimensional fluid-structure interaction problems

MATHICSE Technical Report : A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

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

Reduced basis method for multi-parameter dependent steady Navier-Stokes equations: applications to natural convection in a cavity

Parallel subdomain solver strategies for the algebraic additive Schwarz preconditioner

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

Multiphysics Computational Modeling in C-Heart

Multi space reduced basis preconditioners for large-scale parametrized PDEs

Reduced Basis Methods and A Posteriori Error Estimators for Heat Transfer Problems

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

DeepBND: A machine learning approach to enhance multiscale solid mechanics

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

Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

MATHICSE Technical Report : Multi space reduced basis preconditioners for parametrized Stokes equations

Fluid Structure Interaction Simulations of Physiological Blood Flow in the Aorta