Publications de Simone Deparis

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Interest in patient-specific blood-flow circulation modeling has increased substantially in recent years. The availability of clinical data for geometric and elastic properties together with efficient numerical methods has now made model rendering feasible ...

The goal of this work is to investigate the ability of transfer learning (TL) and multitask learning (MTL) algorithms to predict tasks related to myocardial infarction (MI) in a small-data regime, leveraging a larger dataset of haemodynamic targets. The da ...

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 reduced basis (aLS-RB) method, and improves the existing RB methods for Stokes equations in several directions. First of all, it does not require to enrich the velocity space, as often done when dealing with a velocitypressure formulation, relying on a Pet

This paper presents a spline-based hexahedral mesh generator for tubular geometries commonly encountered in hæmodynamics studies, in particular coronary arteries. We focus on techniques for accurately meshing vessels with stenoses and aneurysms, as well as ...

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

We consider linear and nonlinear convergence acceleration techniques in the framework of Newton or inexact Newton methods. The proposed procedure is based on a new dynamic preconditioner to be used in combination with the GMRES method for reducing the cost of solving a sequence of linear systems. A nonlinear convergence acceleration technique based on a previous work by Washio et al. is also added. The benefits of this combination of acceleration techniques is shown on fluid-structure interaction problems i

We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used ...

The increasing computational load required by most applications and the limits in hardware performances affecting scientific computing contributed in the last decades to the development of parallel software and architectures. In Fluid-Structure Interaction ...

Any solution of the Navier–Stokes equations in a three-dimensional axisymmetric domain admits a Fourier expansion with respect to the angular variable, and it can be noted that each Fourier coefficient satisfies a variational problem on the meridian domain ...

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

We consider the Rosenbrock methods, namely a family of methods for Differential Algebraic Equations, for the solution of the unsteady three-dimensional Navier-Stokes equations. These multistage schemes are attractive for non-linear problems because they ac ...

In this paper we propose a rescaled localized radial basis function (RL-RBF) interpolation method, based on the use of compactly supported radial basis functions. Starting from the classical RBF interpolation technique, we introduce a rescaling that allows ...

We consider the Stokes problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian d ...

We consider the Stokes problem in an axisymmetric three-dimensional domain with data which are axisymmetric and have angular component equal to zero. We observe that the solution is also axisymmetric and the velocity has also zero angular component, hence ...

In this note, we propose Steklov-Poincaré iterative algorithms (mutuated from the analogy with heterogeneous domain decomposition) to solve fluidstructure interaction problems. Although our framework is very general, the driving application is concerned with the interaction of blood flow and vessel wall in large arteries.

LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing faciliti ...

In this paper we review some classical algorithms for fluid-structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory. This approach yields preconditioned Richardson iterations on the Steklov-Poinc ...

As engineering educators pivot towards implementing evidence-based pedagogical strategies, group work - or collaborative work - is being increasingly used in undergraduate classrooms. In mathematics, collaboration is a crucial disciplinary practice. Partic ...

In this note we review some classical algorithms for fluid-structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory. This approach yields preconditioned Richardson iterations on the Steklov-Poinca ...

Simone Deparis

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Physiological simulation of blood flow in the aorta: comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models

Can Knowledge Transfer Techniques Compensate for the Limited Myocardial Infarction Data by Leveraging Haemodynamics? An in silico Study

MATHICSE Technical Report : An algebraic least squares reduced basis method for the solution of parametrized Stokes equations

A spline-based hexahedral mesh generator for patient-specific coronary arteries

Data driven approximation of parametrized PDEs by reduced basis and neural networks

Connecting Ventricular Assist Devices to the Aorta: a Numerical Model

A dynamic preconditioner for Newton-Krylov algorithms. Application to fluid-structure interaction

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

An Efficient Discretization of the Navier–Stokes Equations in an Axisymmetric Domain. Part 1: The Discrete Problem and its Numerical Analysis

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Application of the Rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations

A Rescaled Localized Radial Basis Function Interpolation On Non-Cartesian And Nonconforming Grids

A truncated Fourier/finite element discretization of the Stokes equations in an axisymmetric domain

Weighted Clément operator and application to the finite element discretization of the axisymmetric Stokes problem

Heterogeneous domain decomposition methods for fluid-structure interaction problems

The LifeV library: engineering mathematics beyond the proof of concept

Fluid-structure algorithms based on Steklov-Poincaré operators

Reluctance Despite Recognition: Student Perceptions of Benefits of Group Work

A domain decomposition framework for fluid-structure interaction problems