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170 results on '"Grandmont, Céline"'

1. Numerical analysis of an incompressible soft material poromechanics model using $\protect \tt {T}$-coercivity

Author

Barré, Mathieu, Grandmont, Céline, and Moireau, Philippe

Subjects
Poromechanics, mixture theory, incompressible limit, total discretization, inf-sup stability, energy preserving time-scheme, Materials of engineering and construction. Mechanics of materials, TA401-492
Abstract

This article is devoted to the numerical analysis of the full discretization of a generalized poromechanical model resulting from the linearization of an initial model fitted to soft tissue perfusion. Our strategy here is based on the use of energy-based estimates and $\tt {T}$-coercivity methods, so that the numerical analysis benefits from the essential tools used in the existence analysis of the continuous-time and continuous-space formulation. In particular, our $\tt {T}$-coercivity strategy allows us to obtain the necessary inf-sup condition for the global system from the inf-sup condition restricted to a subsystem having the same structure as the Stokes problem. This allows us to prove that any finite element pair adapted to the Stokes problem is also suitable for this global poromechanical model regardless of porosity and permeability, generalizing previous results from the literature studying this model.

Published
2023
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5. On an existence theory for a fluid-beam problem encompassing possible contacts

Author

Casanova, Jean-Jérôme, Grandmont, Céline, and Hillairet, Matthieu

Subjects
Mathematics - Analysis of PDEs
Abstract

In this paper we consider a coupled system of pdes modelling the interaction between a two--dimensional incompressible viscous fluid and a one--dimensional elastic beam located on the upper part of the fluid domain boundary. We design a functional framework to define weak solutions in case of contact between the elastic beam and the bottom of the fluid cavity. We then prove that such solutions exist globally in time regardless a possible contact by approximating the beam equation by a damped beam and letting this additional viscosity vanish.

Published
2019

6. INSPIRE: A European training network to foster research and training in cardiovascular safety pharmacology

Author

Guns, Pieter-Jan D., Guth, Brian D., Braam, Stefan, Kosmidis, Georgios, Matsa, Elena, Delaunois, Annie, Gryshkova, Vitalina, Bernasconi, Sylvain, Knot, Harm J., Shemesh, Yair, Chen, Alon, Markert, Michael, Fernández, Miguel A., Lombardi, Damiano, Grandmont, Céline, Cillero-Pastor, Berta, Heeren, Ron M.A., Martinet, Wim, Woolard, Jeanette, Skinner, Matt, Segers, Vincent F.M., Franssen, Constantijn, Van Craenenbroeck, Emeline M., Volders, Paul G.A., Pauwelyn, Thomas, Braeken, Dries, Yanez, Paz, Correll, Krystle, Yang, Xi, Prior, Helen, Kismihók, Gábor, De Meyer, Guido R.Y., and Valentin, Jean-Pierre

Published
2020
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9. Stability estimates for a Robin coefficient in the two-dimensional Stokes system

Author

Boulakia, Muriel, Egloffe, Anne-Claire, and Grandmont, Celine

Subjects
Mathematics - Analysis of PDEs
Abstract

In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first study the identifiability of the Robin coefficient and then we establish a stability estimate of logarithm type thanks to a Carleman inequality due to A. L. Bukhgeim and under the assumption that the velocity of a given reference solution stays far from 0 on a part of the boundary where Robin conditions are prescribed.

Published
2012

14. Numerical analysis of an incompressible soft material poromechanics model using T-coercivity

Author

Barré, Mathieu, Grandmont, Céline, Moireau, Philippe, Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Département de Mathématique [Bruxelles] (ULB), Faculté des Sciences [Bruxelles] (ULB), Université libre de Bruxelles (ULB)-Université libre de Bruxelles (ULB), and Sorbonne Université (SU)

Subjects
inf-sup stability, [PHYS.MECA.MEMA]Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph], mixture theory, energy preserving scheme, total discretization, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], incompressible limit
Abstract

This article is devoted to the numerical analysis of the full discretization of a generalized poromechanical model resulting from the linearization of an initial model fitted to soft tissue perfusion. Our strategy here is based on the use of energy-based estimates and T-coercivity methods, so that the numerical analysis benefits from the essential tools used in the existence analysis of the continuous-time and continuous-space formulation. In particular, our T-coercivity strategy allows us to obtain the necessary inf-sup condition for the global system from the inf-sup condition restricted to a subsystem having the same structure as the Stokes problem. This allows us to prove that any finite element pair adapted to the Stokes problem is also suitable for this global poromechanical model regardless of porosity and permeability, generalizing previous results from the literature studying this model.

Published
2023

17. Numerical approximation of the Poisson problem with small holes, using augmented finite elements and defective boundary conditions

Author

Boulakia, Muriel, Grandmont, Céline, Lespagnol, Fabien, Zunino, Paolo, Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Sorbonne Université (SU), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Département de Mathématique [Bruxelles] (ULB), Faculté des Sciences [Bruxelles] (ULB), Université libre de Bruxelles (ULB)-Université libre de Bruxelles (ULB), Laboratorio di Modellistica e Calcolo Scientifico MOX (Dipartimento di Matematica 'Francesco Brioschi'), Politecnico di Milano [Milan] (POLIMI), and Fabien Lespagnol is supported by the project A new computational approach for the fluid-structure in-teraction of slender bodies immersed in three-dimensional flows granted by the Università Italo-Francese, in the framework Vinci 2019.

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

We consider the Poisson problem in a domain with small holes, as a template for developing efficient and accurate numerical approximation schemes for partial differential equations defined on domains with low-dimensional inclusions, such as embedded fibers. We propose a reduced model based on the projection of Dirichlet boundary constraints on a finite dimensional approximation space, obtaining in this way a Poisson problem with defective interface conditions. We analyze the existence of the solution of the reduced problem and for arbitrarily small holes we prove its convergence towards the original problem, the rate of which depends on the size of the inclusion and on the number of modes of the finite dimensional space. The numerical discretization of the reduced problem is addressed by the finite element method, using a computational mesh that does not fit to the holes in the framework of a fictitious domain approach. We propose a stable, optimally convergent and robust formulation with respect to the hole size that exploits an augmented Galerkin formulation based on the addition of suitable non-polynomial functions to the finite element approximation space. The properties of the discretization method are supported by numerical experiments.

Published
2023

18. A coupled model for the dynamics of gas exchanges in the human lung with Haldane and Bohr's effects

Author

Boudin, Laurent, Grandmont, Céline, Grec, Bérénice, Martin, Sébastien, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), and Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [SDV.MHEP.PSR]Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract
Abstract

We propose an integrated dynamical model for oxygen and carbon dioxide transfer from the lung into the blood, coupled with a lumped mechanical model for the ventilation process, for healthy patients as well as in pathological cases. In particular, we focus on the Bohr and Haldane effects, which induce a nonlinear coupling between the oxygen and the carbon dioxide. We also take into account the dead space volume, which requires a special attention in the pathological cases.

Published
2022

21. Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials.

Author

Barré, Mathieu, Grandmont, Céline, and Moireau, Philippe

Subjects
POROUS materials, NUMERICAL analysis, POROELASTICITY, MATHEMATICAL analysis, POROSITY
Abstract

In this work, we thoroughly analyze the linearized version of a poromechanics model developed to simulate soft tissues perfusion. This is a fully unsteady model in which the fluid and solid equations are strongly coupled through the interstitial pressure. As such, it generalizes Darcy, Brinkman and Biot equations of poroelasticity. The mathematical and numerical analysis of this model was initially performed for a compressible porous material. Here, we focus on the nearly incompressible case with a semigroup approach, which also allows us to prove the existence of weak solutions. We show the existence and uniqueness of strong and weak solutions in the incompressible limit case, for which a divergence constraint on the mixture velocity appears. Due to the special form of the coupling, the underlying problem is not coercive. Nevertheless, by using the notion of $ T $-coercivity, we obtain stability estimates and well-posedness results. Our study also provides guidelines to propose stable and robust approximations of the problem with mixed finite elements. In particular, we recover an inf-sup condition that is independent of the porosity. Finally, we numerically investigate the elliptic regularity of the associated steady-state problem and illustrate the sensitivity of the solution with respect to the different model parameters. [ABSTRACT FROM AUTHOR]

Published
2023
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22. Reduced models for the Poisson problem in perforated domains

Author

Boulakia, Muriel, Grandmont, Céline, Lespagnol, Fabien, Zunino, Paolo, Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Département de Mathématique [Bruxelles] (ULB), Faculté des Sciences [Bruxelles] (ULB), Université libre de Bruxelles (ULB)-Université libre de Bruxelles (ULB), Laboratorio di Modellistica e Calcolo Scientifico MOX (Dipartimento di Matematica 'Francesco Brioschi'), Politecnico di Milano [Milan] (POLIMI), and Fabien Lespagnol is supported by the project A new computational approach for the fluid-structure in-teraction of slender bodies immersed in three-dimensional flows granted by the Università Italo-Francese, in the framework Vinci 2019.

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

We develop a fictitious domain method to approximate a Dirichlet problem on a domain with small circular holes (simply called a perforated domain). To address the case of many small inclusions or exclusions, we propose a reduced model based on the projection of the homogeneous Dirichlet boundary constraint on a finite dimensional approximation space. We analyze the existence of the solution of this reduced problem and prove its convergence towards the limit problem without holes. We next obtain an estimate of the gap between the solution of the reduced model and the solution of the full initial model with small holes, the convergence rate depending on the size of the inclusion and on the number of modes of the finite dimensional space. The numerical discretization of the reduced problem is addressed by the finite element method, using a computational mesh that does not fit to the holes. The approximation properties of the finite element method are analyzed by a-priori estimates and confirmed by numerical experiments. elliptic differential equations, small inclusions, asymptotic analysis, approximated numerical method.

Published
2021

23. Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials

Author

Barré, Mathieu, Grandmont, Céline, Moireau, Philippe, Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Département de Mathématique [Bruxelles] (ULB), Faculté des Sciences [Bruxelles] (ULB), Université libre de Bruxelles (ULB)-Université libre de Bruxelles (ULB), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Sorbonne Université (SU), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Grandmont, Celine

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH] Mathematics [math], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math]
Abstract

International audience; In this paper, we thoroughly analyze the linearized version of a poromechanics model developed to simulate biological tissues perfusion. This is a fully dynamical model in which the fluid and solid equations are strongly coupled through the interstitial pressure. As such, it generalizes Darcy, Brinkman and Biot equations of poroelasticity. The mathematical and numerical analysis of this model was first performed for a compressible porous material. Here, we focus on the nearly incompressible case with a semigroup approach that also enables to prove the existence of weak solutions. We show the existence and uniqueness of strong and weak solutions in the incompressible limit, for which a non-standard divergence constraint arises. Due to the special form of the coupling, the underlying problem is not coercive. Nevertheless, by using the notion of T-coercivity, we obtain stability estimates and well-posedness results. Our study also provides guidelines to propose a stable and robust approximation of the problem with mixed finite elements. In particular, we recover an inf-sup condition independent of the phase field. Finally, we investigate numerically the elliptic regularity of the associated steady-state problem and illustrate the sensitivity of the solution with respect to the different model parameters.

Published
2021
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26. Indicateurs de suivi de l'activité scientifique de l'Inria

Author

Brotcorne, Luce, Canteaut, Anne, Viana, Aline, Grandmont, Céline, Guedj, Benjamin, Huot, Stéphane, Issarny, Valérie, Pallez, Guillaume, Perrier, Valérie, Quema, Vivien, Pomet, Jean-Baptiste, Rival, Xavier, Salvati, Sylvain, Thomé, Emmanuel, Integrated Optimization with Complex Structure (INOCS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), inTeRnet BEyond the usual (TRiBE ), Inria Saclay - Ile de France, COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Technology and knowledge for interaction (LOKI), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Middleware on the Move (MIMOVE), Topology-Aware System-Scale Data Management for High-Performance Computing (TADAAM), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Laboratoire d'Informatique de Grenoble (LIG), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Mathematics for Control, Transport and Applications (McTAO), Inria Sophia Antipolis - Méditerranée (CRISAM), Analyse Statique par Interprétation Abstraite (ANTIQUE), Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), Linking Dynamic Data (LINKS), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Inria, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-École polytechnique universitaire de Lille (Polytech Lille), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Inria Bordeaux - Sud-Ouest, Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris, Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Canteaut, Anne

Subjects
[MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO], [MATH.MATH-HO] Mathematics [math]/History and Overview [math.HO], [INFO.INFO-GL]Computer Science [cs]/General Literature [cs.GL], [INFO.INFO-GL] Computer Science [cs]/General Literature [cs.GL]
Abstract

La Commission d'Evaluation de l'Inria a mis en place début 2020, à la demande de la Direction Générale, un groupe de travail visant à réfléchir à des indicateurs pour l'analyse qualitative de l'activité scientifique de l'Institut. Ce document est le fruit des discussions de ce groupe, enrichies par les échanges avec la Direction Générale d'Inria et avec l'ensemble de la Commision d'Evaluation. Au-delà de cette « commande », il nous a semblé important de saisir cette opportunité pour mener une réflexion collective, qui dépasse le cadre de notre Institut, sur les indicateurs, et sur ce qu'ils peuvent ou ne peuvent pas dire de nos pratiques scientifiques.

Published
2020

27. Existence and uniqueness for a quasi-static interaction problem between a viscous fluid and an active structure

Author

Grandmont, Céline, Vergnet, Fabien, COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
Fluid-structure interaction, Strong solution, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Existence result, Active structure
Abstract

International audience; We consider a quasi-static fluid-structure interaction problem where the fluid is modeled by theStokes equations and the structure is an active and elastic medium. More precisely, the displacementof the structure verifies the equations of elasticity with an active stress, which models the presenceof internal biological motors in the structure. Under smallness assumptions on the data, we provethe existence of a unique solution for this strongly coupled system.

Published
2020
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32. Editorial CEMRACS 2018

Author

Calvez Vincent, Grandmont Céline, Lochërbach Eva, Poignard Clair, Ribot Magali, and Vauchelet Nicolas

Subjects
T57-57.97, Applied mathematics. Quantitative methods, QA1-939, Mathematics
Published
2020

38. A multi-scale epidemic model of Salmonella infection with heterogeneous shedding.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Labarthe, Simon, Laroche, Béatrice, Nguyen, Thi Nhu Tao, Polizzi, Bastien, Patout, Florian, and Stegmaier, Tabea

Subjects
*SALMONELLA, *MULTISCALE modeling, *PATHOGENIC bacteria, *VETERINARY bacteriology, *COMPUTER simulation
Abstract

Salmonella strains colonize the digestive tract of farm livestock, such as chickens or pigs, without affecting them, and potentially infect food products, representing a threat for human health ranging from food poisoning to typhoid fever. It has been shown that the ability to excrete the pathogen in the environment and contaminate other animals is variable. This heterogeneity in pathogen carriage and shedding results from interactions between the host's immune response, the pathogen and the commensal intestinal microbiota. In this paper we propose a novel generic multiscale modeling framework of heterogeneous pathogen transmission in an animal population. At the intra-host level, the model describes the interaction between the commensal microbiota, the pathogen and the inflammatory response. Random fluctuations in the ecological dynamics of the individual microbiota and transmission at between-host scale are added to obtain a drift-diffusion PDE model of the pathogen distribution at the population level. The model is further extended to represent transmission between several populations. The asymptotic behavior as well as the impact of control strategies including cleaning and antimicrobial administration are investigated through numerical simulation. [ABSTRACT FROM AUTHOR]

Published
2020
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39. Opinion propagation on social networks: a mathematical standpoint.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Lavenant, H., and Maury, B.

Subjects
*STOCHASTIC analysis, *PARTIAL differential equations, *NONLINEAR analysis, *GAUSSIAN function, *EVOLUTION equations
Abstract

These lecture notes address mathematical issues related to the modeling of opinion propagation on networks of the social type. Starting from the behavior of the simplest discrete linear model, we develop various standpoints and describe some extensions: stochastic interpretation, monitoring of a network, time continuous evolution problem, charismatic networks, links with discretized Partial Differential Equations, nonlinear models, inertial version and stability issues. These developments rely on basic mathematical tools, which makes them accessible at an undergraduate level. In a last section, we propose a new model of opinion propagation, where the opinion of an agent is described by a Gaussian density, and the (discrete) evolution equation is based on barycenters with respect to the Fisher metric. [ABSTRACT FROM AUTHOR]

Published
2020
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40. Comparison and calibration of different electroporation models. Application to rabbit livers experiments.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Jankowiak, Gaspard, Taing, Cécile, and Collin, Annabelle

Subjects
*ELECTROPORATION, *TUMORS, *ELECTRIC fields, *ELECTROPHYSIOLOGY, *COMPUTER simulation of biological systems
Abstract

Electroporation is a complex phenomenon that occurs when biological tissues are subjected to electric pulses. The clinical interest for the phenomenon has constantly increased for the last decades. Indeed, electroporation makes it possible to either kill directly the cells in the target region (tumor) or to introduce molecules into living cells. However, one of the main limitation of using electroporation in the clinical routine comes from the technical difficulties raised by such therapies, in particular it is difficult to well determine the treated zone. Numerical modeling of the electric field magnitude could provide a powerful strategy to assess the treatment efficacy: thanks to well-designed models, the computation of the distribution of the electric field is achievable, providing a numerical evaluation of the treatment. The main objective of this work is to go further on the patient-adapted numerical modeling of the electric field magnitude by laying the ground of the possible electroporation models - which will be compared qualitatively - and their calibrations. This will be done in the framework of bioelectrical measurements on rabbit livers that come from the literature. [ABSTRACT FROM AUTHOR]

Published
2020
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41. Cell migration in complex environments: chemotaxis and topographical obstacles.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Cucchi, Alessandro, Etchegaray, Christèle, Meunier, Nicolas, Navoret, Laurent, and Sabbagh, Lamis

Subjects
*CELL migration, *CELL motility, *TWO-dimensional models, *STOCHASTIC differential equations, *DISCRETE systems
Abstract

Cell migration is a complex phenomenon that plays an important role in many biological processes. Our aim here is to build and study models of reduced complexity to describe some aspects of cell motility in tissues. Precisely, we study the impact of some biochemical and mechanical cues on the cell dynamics in a 2D framework. For that purpose, we model the cell as an active particle with a velocity solution to a particular Stochastic Differential Equation that describes the intracellular dynamics as well as the presence of some biochemical cues. In the 1D case, an asymptotic analysis puts to light a transition between migration dominated by the cell's internal activity and migration dominated by an external signal. In a second step, we use the contact algorithm introduced in [15,18] to describe the cell dynamics in an environment with obstacles. In the 2D case, we study how a cell submitted to a constant directional force that mimics the action of chemoattractant, behaves in the presence of obstacles. We numerically observe the existence of a velocity value that the cell can not exceed even if the directional force intensity increases. We find that this threshold value depends on the number of obstacles. Our result confirms a result that was already observed in a discrete framework in [3,4]. [ABSTRACT FROM AUTHOR]

Published
2020
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42. Modeling and analysis of adipocytes dynamic with a differentiation process.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Gilleron, Jérôme, Goudon, Thierry, Lagoutière, Frédéric, Martin, Hugo, Mauroy, Benjamin, Millet, Pascal, and Vaghi, Cristina

Subjects
*FAT cells, *MESENCHYMAL stem cells, *ADVECTION, *DIFFERENTIAL equations
Abstract

We propose in this article a model describing the dynamic of a system of adipocytes, structured by their sizes. This model takes into account the differentiation of a population of mesenchymal cells into preadipocytes and of preadipocytes into adipocytes; the differentiation rates depend on the mean adipocyte radius. The considered equations are therefore ordinary differential equations, coupled with an advection equation, the growth rate of which depends on food availability and on the total surface of adipocytes. Since this velocity is discontinuous, we need to introduce a convenient notion of solutions coming from Filippov theory. We are consequently able to determine the stationary solutions of the system, to prove the existence and uniqueness of solutions and to describe the asymptotic behavior of solutions in some simple cases. Finally, the parameters of the model are fitted thanks to some experimental data and numerical simulations are displayed; a spatial extension of the model is studied numerically. [ABSTRACT FROM AUTHOR]

Published
2020
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43. Curved interface reconstruction for 2D compressible multi-material flows.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Chollet, Igor, Lissoni, Giulia, Corot, Théo, Hoch, Philippe, Leroy, Thomas, and Dumas, Laurent

Subjects
*DYNAMIC programming, *TWO-dimensional models, *COMPRESSIBLE flow, *ROBUST control
Abstract

In this paper, we describe an interface reconstruction method in two dimension. This method is an extension of DPIR [1], which reconstructs continuous interfaces and preserves partial volumes using dynamic programming. First we extend the method to curved interfaces. Then, we present tools to improve its robustness in order to apply it to unstructured grid. Finally, we describe an extension to three materials. [ABSTRACT FROM AUTHOR]

Published
2020
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44. Horizontal gene transfer: numerical comparison between stochastic and deterministic approaches.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Figueroa Iglesias, Susely, Hivert, Hélène, Méléard, Sylvie, Melnykova, Anna, and Nordmann, Samuel

Subjects
*HORIZONTAL gene transfer, *GENETIC transformation, *DRUG resistance in bacteria, *INTEGRO-differential equations, *HAMILTON-Jacobi equations, *COMPUTER simulation of biological systems
Abstract

Horizontal gene Transfer (HT) denotes the transmission of genetic material between two living organisms, while the vertical transmission refers to a DNA transfer from parents to their offspring. Consistent experimental evidence report that this phenomenon plays an essential role in the evolution of certain bacterias. In particular, HT is believed to be the main instrument of developing the antibiotic resistance. In this work, we consider several models which describe this phenomenon: a stochastic jump process (individual-based) and the deterministic nonlinear integrodifferential equation obtained as a limit for large populations. We also consider a Hamilton-Jacobi equation, obtained as a limit of the deterministic model under the assumption of small mutations. The goal of this paper is to compare these models with the help of numerical simulations. More specifically, our goal is to understand to which extent the Hamilton-Jacobi model reproduces the qualitative behavior of the stochastic model and the phenomenon of evolutionary rescue in particular. [ABSTRACT FROM AUTHOR]

Published
2020
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45. Fluid-kinetic modelling for respiratory aerosols with variable size and temperature.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Boudin, Laurent, Grec, Bérénice, Martin, Sébastien, Mecherbet, Amina, and Noël, Frédérique

Subjects
*AIR flow, *PARTICLES, *RESPIRATORY organs, *NAVIER-Stokes equations, *VLASOV equation, *COMPUTER simulation of biological systems
Abstract

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics. [ABSTRACT FROM AUTHOR]

Published
2020
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46. Construction of a statistical learning tool based on ordinary differential equations to model the digestive behaviour of ross chickens.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Bloyet, Nicolas, Flourent, Hélène, Frénod, Emmanuel, Handa, Marouan, Moundoyi, Harold, and Phuong, Thuy Vo Thi

Subjects
*DOMESTIC animals, *DATA modeling, *ANIMAL feeds, *CHICKENS, *STATISTICAL learning, *APPROXIMATION theory
Abstract

Being able to monitor and forecast farm animal performances is a strategic problem in the agronomy industry. We use a Data-Model Coupling approach to build a biomimetic Statistical Learning tool taking into account some aspects of the biological dynamics of the animal body. The objective is to build a tool which is able to assimilate data about daily feed consumption and measured performances. The model encompasses several sub-models corresponding to compartments and permitting to mimic a kinetic process divided into several steps. Each sub-model contains parameters which can be learnt by using an optimization algorithm and data. The goal of the first application of the model on field data was to simulate and predict the growth of chickens. An experiment was performed during 70 days to collect every day the feed consumption and the weight gain of a male and a female chickens. After the learning of the model parameters, the model shows a very good approximation of the chicken's weight evolution over time. [ABSTRACT FROM AUTHOR]

Published
2020
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47. Geometry description and mesh construction from medical imaging.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Carlino, Michele Giuliano, Ricka, Philippe, Phan, Minh, Bertoluzza, Silvia, Pennacchio, Micol, Patanè, Giuseppe, and Spagnuolo, Michela

Subjects
*IMAGE segmentation, *MESH networks, *ALGORITHMS, *MEDICAL imaging systems, *COMPUTER simulation
Abstract

We present a new method for defining and meshing patient-specific domains from medical images. Our approach is based on an atlas image segmentation technique, and relies on the modular registration algorithm of S. Bertoluzza et al. [25]. The mesh of the patient-specific domain is generated by deforming the corresponding mesh on an a priori segmented and meshed reference image (the atlas). Our method aims at automating the process at the interface of medical imaging and numerical simulation, thus reducing the computational cost in those situations where simulations have to be managed on numerous medical images of similar patients. [ABSTRACT FROM AUTHOR]

Published
2020
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48. Swimming at low Reynolds number.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Berti, Luca, Giraldi, Laetitia, and Prud'homme, Christophe

Subjects
*SWIMMING, *RIGID bodies, *REYNOLDS number, *STOKES equations, *QUATERNIONS
Abstract

We address the swimming problem at low Reynolds number. This regime, which is typically used for micro-swimmers, is described by Stokes equations. We couple a PDE solver of Stokes equations, derived from the Feel++ finite elements library, to a quaternion-based rigid-body solver. We validate our numerical results both on a 2D exact solution and on an exact solution for a rotating rigid body respectively. Finally, we apply them to simulate the motion of a one-hinged swimmer, which obeys to the scallop theorem. [ABSTRACT FROM AUTHOR]

Published
2020
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49. Influence of the mode of reproduction on dispersal evolution during species invasion.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Crevat, Joachim, Dekens, Léonard, Fabrèges, Benoit, Kuczma, Frédéric, Lavigne, Florian, and Raoul, Gaël

Subjects
*REACTION-diffusion equations, *ASEXUAL reproduction, *REPRODUCTION, *HEURISTIC
Abstract

We consider a reaction-diffusion-reproduction equation, modeling a population which is spatially heterogeneous. The dispersion of each individuals is influenced by its phenotype. In the literature, the asymptotic propagation speed of an asexual population has already been rigorously determined. In this paper we focus on the difference between the asexual reproduction case, and the sexual reproduction case, involving a non-local term modeling the reproduction. This comparison leads to a different invasion speed according to the reproduction. After a formal analysis of both cases, leading to a heuristic of the asymptotic behaviour of the invasion fronts, we give some numerical evidence that the acceleration rate of the spatial spreading of a sexual population is slower than the acceleration rate of an asexual one. The main difficulty to get sharper results on a transient comes from the non-local sexual reproduction term. [ABSTRACT FROM AUTHOR]

Published
2020
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50. Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Bonnet, Celine, Chahour, Keltoum, Clément, Frédérique, Postel, Marie, and Yvinec, Romain

Subjects
*OVARIAN follicle, *DIFFERENTIAL equations, *TIMESCALE number, *SINGULAR perturbations
Abstract

In this study, we describe different modeling approaches for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or stochastic (SDE) differential equations, and accounting for interactions between follicles. We put a special focus on representing the population-level feedback exerted by growing ovarian follicles onto the activation of quiescent follicles. We take advantage of the timescale difference existing between the growth and activation processes to apply model reduction techniques in the framework of singular perturbations. We first study the linear versions of the models to derive theoretical results on the convergence to the limit models. In the nonlinear cases, we provide detailed numerical evidence of convergence to the limit behavior. We reproduce the main semi-quantitative features characterizing the ovarian follicle pool, namely a bimodal distribution of the whole population, and a slope break in the decay of the quiescent pool with aging. [ABSTRACT FROM AUTHOR]

Published
2020
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