Florent CHAVE

Postdoctoral researcher in Applied Mathematics
Member of the team-project RAPSODI
INRIA Lille - Nord Europe, France
Supervised by S. Lemaire and E. Creusé

Office: A107
E-mail: florent.chave AT inria.fr
Curriculum vitæ: CV.pdf

Research


11/2018 — PhD thesis: Hybrid High-Order methods interface problems
Manuscript tel-01926061 and defense report DR.pdf
09/2018 — A Hybrid High-Order method for passive transport in fractured porous media
with D. A. Di Pietro and L. Formaggia
International Journal on Geomathematics, 2018. Published online. DOI: 10.1007/s13137-019-0114-x
HAL preprint hal-01784181
11/2017 — A Hybrid High-Order method for flows in fractured porous media
with D. A. Di Pietro and L. Formaggia
SIAM J. Sci. Comput., 2018, 40(2):A1063–A1094. DOI: 10.1137/17M1119500
HAL preprint hal-01482925, arXiv preprint arXiv:1711.11420
02/2017 — A Hybrid High-Order method for the convective Cahn–Hilliard problem in mixed form
with D. A. Di Pietro and F. Marche
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, 2017 p. 517–526
HAL preprint hal-01477247, arXiv preprint arXiv:1702.08224
06/2016 — A Hybrid High-Order method for the Cahn–Hilliard problem in mixed form
with D. A. Di Pietro , F. Marche and F. Pigeonneau
SIAM J. Numer. Anal., 2016, 54(3):1873–1898. DOI: 10.1137/15M1041055
HAL preprint hal-01203733, arXiv preprint arXiv:1509.07384

Presentations


Forthcoming: 04/2019 — Poster session: Reduced models for flow and transport in fractured porous media
POlytopal Element Methods in Mathematics and Engineering, Marseille (CIRM), France
07/2018 — Presentation of a HHO method for flows and passive transport in fractured porous media
Italian Society of Applied and Industrial Mathematics, Rome, Italy
06/2018 — Presentation of a HHO method for flows and passive transport in fractured porous media
International Conference on Boundary and Interior Layers, Glasgow, Scotland
09/2017 — Presentation of a HHO method for Darcy flows in fractured porous media
SIAM Conference on Mathematical and Computational Issues in the Geosciences, Friedrich-Alexander University Erlangen-Nürnberg, Germany
Presentation of a HHO method for Darcy flows in fractured porous media
European Conference on Numerical Mathematics and Advanced Applications, Voss, Norway
08/2017 — Presentation of a HHO method for Darcy flows in fractured porous media
Reliable Methods of Mathematical Modeling 8, Humboldt University of Berlin, Germany
06/2017 — Poster session: A HHO method for the Convective Cahn–Hilliard problem in mixed form
Finite Volumes for Complex Applications 8, University of Lille 1, France
05/2017 — Presentation of a HHO method for Darcy flows in fractured porous media
15th European Finite Element Fair, Polytechnic University of Milan, Italy
01/2017 — Presentation of a HHO method for Darcy flows in fractured porous media
CompGeo - Computational Geosciences @ MOX, Polytechnic University of Milan, Italy
10/2016 — Presentation of a HHO method and application to the Cahn–Hilliard problem
Numerical Methods for PDEs, Institut Henri Poincare, Paris, France
Poster session: A HHO method for Darcy flows in fractured porous media
GdR MaNu - Mathématiques pour le Nucléaire, St Valery sur Somme, France
06/2016 — Presentation of a HHO method and application to the Cahn–Hilliard problem
European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece
05/2016 — Presentation of a HHO method and application to the Cahn–Hilliard problem
14th European Finite Element Fair, University of Bonn, Germany
02/2016 — Presentation of a HHO method and application to the Cahn–Hilliard problem
Groupe de travail - ACSIOM team, University of Montpellier, France
01/2016 — Calculation of shadows and occlusions in a geometric scene, in collaboration with OPTIS
Semaine d'Etude Maths-Entreprises, Sophia Antipolis, France
10/2015 — Poster session: A HHO method for the Cahn–Hilliard problem in mixed form
POlytopal Element Methods in Mathematics and Engineering, Georgia Institute of Technology, Atlanta, GA, USA
09/2015 — Presentation of the development of a HHO method for the Cahn-Hilliard problem
Saint-Gobain Recherche, Aubervilliers, France

Teaching


2018/19 — University of Lille
1st year IMA2A3 (equiv. L3 at Polytech engineering schools) - Numerical Analysis (lectures, tutorials & TP)
2017/18 — University of Montpellier
2nd year PEIP (equiv. L2 at Polytech engineering schools) - Probabilities, Geometry, Topology & Analysis (tutorials)
L1 - Operational research (tutorials)
2016/17 — University of Montpellier
L3 - Numerical analysis of ODEs (TP)
L2 - Introduction to Scientific Software (TP)
L2 - Mathematics for Earth Science (TP)
2015/16 — University of Montpellier
L1 - BioMaths (lectures & tutorials)

Education


Since 12/2018 — Postdoctoral researcher within the team-project RAPSODI at INRIA Lille - Nord Europe, France
Working on high-order polytopal discretization methods for electromagnetism
Supervisors: S. Lemaire and E. Creusé
11/2018 — PhD in Applied Mathematics en cotutelle: University of Montpellier & Polytechnic University of Milan
PhD thesis: Hybrid High-Order methods for interface problems (TEL tel-01926061 and defense report DR.pdf)
Supervisors: D. A. Di Pietro and L. Formaggia
08/2015 — Master's degree of Applied Mathematics, University of Montpellier, France
Master thesis: Development of a HHO method for the Cahn-Hilliard problem
Supervisors: D. A. Di Pietro and F. Marche
06/2013 — Bachelor's degree of Pure and Applied Mathematics, University of Montpellier, France

Outputs


Meshes — Nonconforming mesh refinement of the 2 dimensional square unit (.typ1 format)
  > mesh5_1  (h = 6.25e-02)
> mesh5_2  (h = 3.12e-02)
> mesh5_3  (h = 1.56e-02)
> mesh5_4  (h = 7.81e-03)
> mesh5_5  (h = 3.91e-03)
> mesh5_6  (h = 1.95e-03)
Numerical experiments
Passive transport in fractured porous media
We consider horizontal fractures that act as barriers.
> Link to the video
We consider here vertical fractures that act as conduits.
> Link to the video
Cahn-Hilliard
We perturb the steady solution in order to show the robustness of the method to capture the interface dynamics subject to a strong circular velocity fields.
> Link to the video
We compare three evolutions of the same initial condition, obtained on different Cartesian meshes (128x128, 64x64, 32x32) and different polynomial degrees (0,1,2). The initial condition is a random value between +/- 1 inside each element of the 32x32 Cartesian mesh.
> Link to the video
We compare four evolutions of the same initial condition, obtained with different Peclet number. The initial condition is a random value between +/- 1 on each cells that are inside a circular domain of the Voronoi mesh and -1 outside.
> Link to the video