Franz Chouly

Professor
Universidad de la Republica Uruguay

Montevideo URUGUAY

Email : fchouly-at-cmat.edu.uy / franz.chouly-at-math.cnrs.fr

Curriculum vitae

Research interests

My research is focused on numerical analysis and scientific computing, with emphasis on finite element methods and boundary/interface conditions such as it occurs in fluid-structure interaction and contact/friction. It encompasses both theoretical aspects (proofs of stability and accuracy) and applied aspects, with interdisciplinary and industrial collaborations. Main applications fields are solid/fluid mechanics and biomechanics. 

A book on finite element methods for contact and friction is available here.

An overview of my research on Nitsche’s method for contact and friction is available here.

A success story of collaboration between mathematics and spinoffs (TexiSense/TwinSight) is available here (see also AMIES/EuMathIn websites).

Post-doctoral supervision

1. Huu Phuoc Bui (2017) Goal oriented a posteriori error estimation for hyperelastic contractile models applied to clinical biomechanics. Grant from the Agence Maths Entreprises (AMIES) and partnership with Marek Bucki (TexiSense, Grenoble).

PhD students

1. Johan Marguet. Université de Franche-Comté (2023-2026). Numerical methods for convection-dominated and nonlocal models in biology. Co-advisors : Raluca Eftimie, Alexei Lozinski.
   webpage
2. Hao Huang. Université de Bourgogne (2021-2024). Numerical methods for non-regular elastodynamics. Co-advisors : Guillaume Drouet, Nicolas Pignet.
   webpage
3. Raphaël Bulle. Université du Luxembourg + Université Bourgogne Franche-Comté (2017-2022). A posteriori error estimation for finite element approximations of fractional Laplacian problems and applications to poro-elasticity. Co-advisors : Stéphane Bordas, Jack Hale, Alexei Lozinski.
   webpage / document
4. Rabii Mlika. INSA Lyon (2015-2018). Nitsche method for frictional contact and self-contact : mathematical and numerical study. Co-advisor : Yves Renard.
   webpage / document
5. Michel Duprez. Université de Franche-Comté (2012-2015). Controllability of some parabolic systems. Co-advisor : Farid Ammar Khodja.
   webpage / document
6. Nicolas Hermant. Grenoble-INP (2011-2014). Observation, modeling and simulation of the vibrations of a vocal folds replica with application to pathological configurations. Co-advisors : Xavier Pelorson, Fabrice Silva.
   webpage / document

Books

1. Error control, adaptive discretizations, and applications, part 1.
   F. Chouly, S.P.A. Bordas, R. Becker & P. Omnes. Elsevier, to appear.
   website
2. Finite element approximation of contact and friction in elasticity.
   F. Chouly, P. Hild & Y. Renard. Springer / Birkhäuser, 2023.
   DOI:10.1007/978-3-031-31423-0

Theses

1. Contributions au traitement des conditions limites et d’interface dans le cadre de la Méthode des Eléments Finis.
   F. Chouly. Habilitation à Diriger des Recherches de l’U.F.C. , Besançon, France. 12/2013.
   document
2. Modélisation physique des voies aériennes supérieures pour le Syndrome d’Apnées Obstructives du Sommeil.
   F. Chouly. Thèse de Doctorat de l’I.N.P.G. , Grenoble, France. 12/2005.
   document

Preprints / submitted articles or notes

1. Automatic mesh refinement for soft tissue.
   H.P. Bui, M. Duprez, P.Y. Rohan, A. Lejeune, S.P.A. Bordas, M. Bucki & F. Chouly. Submitted.
   preprint
2. Stokes problem with slip boundary conditions using stabilized finite elements combined with Nitsche.
   R. Araya, A. Caiazzo & F. Chouly. Submitted.
   preprint
3. A review on some discrete variational techniques for the approximation of essential boundary conditions.
   F. Chouly. Submitted.
   preprint

International Journals

1. HHT-alpha and TR-BDF2 schemes for dynamic contact problems.
   H. Huang, N. Pignet, G. Drouet & F. Chouly. Comput. Mech. To appear.
   preprint
2. Modelling keloid dynamics: a brief review and new mathematical perspectives.
   R. Eftimie, G. Rolin, O. Adebayo, S. Urcun , F. Chouly & S.P.A. Bordas. Bull. Math. Biol. Vol. 85, article no. 117, 2023.
   preprint
3. Residual a posteriori error estimation for frictional contact with Nitsche method.
   R. Araya & F. Chouly. J. Sci. Comput. Vol. 96, paper no. 87, 2023.
   preprint
4. Mixed and Nitsche's discretizations of Coulomb frictional contact-mechanics for mixed dimensional poromechanical models.
   L. Beaude, F. Chouly, M. Laaziri & R. Masson. Comput. Methods Appl. Mech. Engrg. Vol. 413, paper no. 116124, 2023.
   preprint
5. A Nitsche method for the elastoplastic torsion problem.
   F. Chouly, T. Gustafsson & P. Hild.  ESAIM : Math. Model. Numer. Anal. Vol 57, pp.1731-1746, 2023.
   preprint
6. An a posteriori error estimator for the spectral fractional power of the Laplacian.
   R. Bulle, O. Barrera, S.P.A. Bordas, F. Chouly & J.S. Hale. Comput. Methods Appl. Mech. Engrg. Vol. 407, paper no. 115943, 2023.
   preprint
7. Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project.
   R. Bulle, J.S. Hale, A. Lozinski, S.P.A. Bordas & F. Chouly. Comput. Math. Appl. Vol. 131, pp.103-123, 2023.
   preprint
8. Nitsche method for contact with Coulomb friction: existence results for the static and dynamic finite element formulations.
   F. Chouly, P. Hild, V. Lleras & Y. Renard. J. Comput. Appl. Math. Vol. 416, paper no. 114557, 2022.
   preprint
9. On a finite element approximation for the elastoplastic torsion problem.
   F. Chouly & P. Hild. Appl. Math. Lett. Vol. 132, paper no. 108191, 2022.
   preprint
10. Wave-heat coupling in one-dimensional unbounded domains: artificial boundary conditions and an optimized Schwarz method.
    F. Chouly & P. Klein. Numer. Algorithms. Vol. 90, pp.631-668, 2022.
    preprint
11. Hybrid High-Order discretizations combined with Nitsche's method for Dirichlet and Signorini boundary conditions.
    K. Cascavita, F. Chouly & A. Ern. IMA J. Numer. Anal. Vol. 40, pp. 2189-2226, 2020.
    preprint
12. An open source pipeline for design of experiments for hyperelastic models of the skin with applications to keloids.
    D. Sutula, A. Elouneg, M. Sensale, F. Chouly, J. Chambert, A. Lejeune, D. Baroli, P. Hauseux, S.P.A. Bordas & E. Jacquet. J. Mech. Behav. Biomed. Vol. 112, Article 103999, 2020.
    article
13. A Hybrid High-Order discretization combined with Nitsche's method for contact and Tresca friction in small strain elasticity.
    F. Chouly, A. Ern & N. Pignet. SIAM J. Sci. Comput. Vol. 42, pp. A2300-2324, 2020.
    preprint
14. Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three.
    R. Bulle, F. Chouly, J.S. Hale & A. Lozinski.  Appl. Math. Lett. Vol. 107, Article 106429, 2020.
    preprint
15. Quantifying discretization errors for soft-tissue simulation in computer assisted surgery : a preliminary study.
    M. Duprez, S.P.A. Bordas, M. Bucki, H.P. Bui, F. Chouly, V. Llleras, C. Lobos, A. Lozinski, P.-Y. Rohan & S. Tomar. Appl. Math. Model. Vol. 77, Num. 1, pp. 709-723, 2020.
    preprint
16. Explicit Verlet time-integration for a Nitsche-based approximation of elastodynamic contact problems.
    F. Chouly & Y. Renard.  Adv. Model. and Simul. in Eng. Sci. Vol. 5, pp. 1-38, 2018.
    preprint
17. Analysis of a stabilized penalty-free Nitsche method for the Brinkman, Stokes and Darcy problems.
    L. Blank, A. Caiazzo, F. Chouly, A. Lozinski & J. Mura. ESAIM : Math. Model. Numer. Anal. Vol. 52, pp. 2149-2185, 2018.
    preprint
18. Skew-symmetric Nitsche’s formulation in isogeometric analysis : Dirichlet and symmetry conditions, patch coupling and frictionless contact.
    Q. Hu, F. Chouly, P. Hu, G. Cheng & S.P.A. Bordas. Comput. Methods Appl. Mech. Engrg. Vol. 341, pp. 188-220, 2018.
    preprint
19. An unbiased Nitsche’s approximation of the frictional contact between two elastic structures.
    F. Chouly, R. Mlika & Y. Renard. Numer. Math. Vol. 139, pp. 593-631, 2018.
    preprint
20. Numerical study of the vibrations of an elastic container filled with an inviscid fluid.
    N. Hermant, F. Chouly, F. Silva & P. Luizard. ZAMM Z. Angew. Math. Mech.. Vol. 98, pp. 602-621, 2018.
    preprint
21. Residual-based a posteriori error estimation for contact problems approximated by Nitsche’s method.
    F. Chouly, M. Fabre, P. Hild, J. Pousin & Y. Renard. IMA J. Numer. Anal. Vol. 38, pp. 921-954, 2018.
    preprint
22. A clustering package for nucleotide sequences using Laplacian Eigenmaps and Gaussian Mixture Models.
    M. Bruneau, T. Mottet, S. Moulin, M. Kerbiriou, F. Chouly, S. Chrétien & C. Guyeux. Comput. Biol. Med. Vol. 93, pp. 66-74, 2018.
    preprint
23. An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact.
    R. Mlika, Y. Renard & F. Chouly. Comput. Methods Appl. Mech. Engrg. Vol. 325, pp. 265-288, 2017.
    preprint
24. Partial null controllability of parabolic linear systems.
    F. Ammar Khodja, F. Chouly & M. Duprez. Math. Control Relat. Fields. Vol. 6, pp.185-216, 2016.
    preprint
25. A time-parallel framework for coupling finite element and lattice Boltzmann methods.
    M. Astorino, F. Chouly & A. Quarteroni. Appl. Math. Res. Express. AMRX. Vol. 2016, pp. 24-67, 2016.
    preprint
26. A Nitsche finite element method for dynamic contact : 2. Stability of the schemes and numerical experiments.
    F. Chouly, P. Hild & Y. Renard. ESAIM : Math. Model. Numer. Anal. Vol. 49, pp. 503-528, 2015.
    preprint
27. A Nitsche finite element method for dynamic contact : 1. Semi-discrete problem analysis and time-marching schemes.
    F. Chouly, P. Hild & Y. Renard. ESAIM : Math. Model. Numer. Anal. Vol. 49, pp. 481-502, 2015.
    preprint
28. Symmetric and non-symmetric variants of Nitsche’s method for contact problems in elasticity : theory and numerical experiments.
    F. Chouly, P. Hild & Y. Renard. Math. Comp. Vol. 84, pp. 1089-1112, 2015.
    preprint
29. An adaptation of Nitsche’s method to the Tresca friction problem.
    F. Chouly. J. Math. Anal. Appl. Vol. 411 , pp. 329-339 , 2014.
    preprint
30. A Nitsche-based method for unilateral contact problems : numerical analysis.
    F. Chouly & P. Hild. SIAM J. Numer. Anal. Vol. 51, Num. 2, pp. 1295–1307, 2013.
    preprint
31. On convergence of the penalty method for unilateral contact problems.
    F. Chouly & P. Hild. Appl. Num. Math. Vol. 65, pp. 27-40, 2013.
    preprint
32. A local projection stabilized method for fictitious domains.
    G.-R. Barrenechea & F. Chouly. Appl. Math. Lett. Vol. 25, Num. 12, pp. 2071-2076, 2012.
    preprint
33. Comparison of computations of asymptotic flow models in a constricted channel. 
    F. Chouly & P.-Y. Lagrée. Appl. Math. Model. Vol. 36, Num. 12, pp. 6061–6071, 2012.
    preprint
34. A Nitsche-based domain decomposition method for hypersingular integral equations. 
    F. Chouly & N. Heuer. Numer. Math. Vol. 121, Num. 4, pp. 705-729, 2012. 
    preprint
35. Robin based semi-implicit coupling in fluid-structure interaction : stability analysis and numerics.
    M. Astorino, F. Chouly & M.-A. Fernández. SIAM J. Sci. Comput., Vol. 31, Num. 6, pp. 4041-4065, 2009.
    preprint
36. A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations.
    G.-R. Barrenechea & F. Chouly. ZAMM Z. Angew. Math. Mech., Vol. 89, Num. 1, pp. 54-68, 2009.
    preprint
37. Modelling the human pharyngeal airway : validation of numerical simulations using in-vitro experiments.
    F. Chouly, A. Van Hirtum, P.-Y. Lagrée, X. Pelorson & Y. Payan. Med. Biol. Eng. Comput., Vol. 47, pp. 49-58, 2009. 
    preprint
38. Numerical and experimental study of expiratory flow in the case of major upper airway obstructions with fluid-structure interaction. 
    F. Chouly, A. Van Hirtum, P.-Y. Lagrée, X. Pelorson & Y. Payan. J. Fluid. Struct. , Vol. 24, pp. 250-269, 2008. 
    preprint

Conference Proceedings (in books, with peer-review)

1. HHT-alpha and TR-BDF2 schemes for Nitsche-based discrete dynamic contact.
   H. Huang, N. Pignet & F. Chouly. Lect. Notes Comput. Sci. Eng. To appear.
   Proceedings of the European Conference on Numerical Mathematics and Advanced Applications ENUMATH 2023.
   preprint
2. Mixed and Nitsche's discretizations of frictional contact-mechanics in fractured porous media.
   L. Beaude , F. Chouly, M. Laaziri & R. Masson. Lect. Notes Comput. Sci. To appear.
   Proceedings of the 14th International Conference on Large-Scale Scientific Computations, 2023.
   preprint
3. Nitsche-based finite element method for contact with Coulomb friction.
   F. Chouly, P. Hild, V. Lleras & Y. Renard. Lect. Notes Comput. Sci. Eng. Vol. 126, pp. 839-847, 2019.
   Proceedings of the European Conference on Numerical Mathematics and Advanced Applications ENUMATH 2017. Editors : Florian A. Radu, Kundan Kumar, Inga Berre, Jan M. Nordbotten, Iuliu S. Pop.
   preprint
4. An overview of recent results on Nitsche’s method for contact problems.
   F. Chouly, M. Fabre, P. Hild, R. Mlika, J. Pousin & Y. Renard. Lect. Notes Comput. Sci. Eng. Vol. 121, pp. 93-141, 2017.
   Proceedings of the UCL Workshop 2016 on Geometrically Unfitted Finite Element Methods and Applications. Editors : Stéphane Bordas, Erik Burman, Mats G. Larson and Maxim Olshanskii.
   preprint
5. Simulation of the retroglossal fluid-structure interaction during Obstructive Sleep Apnea. 
   F. Chouly, A. Van Hirtum, P.-Y. Lagrée, J.-R. Paoli, X. Pelorson & Y. Payan. Lect. Notes Comput. Sci. Vol. 4072, pp. 48-57, 2006.
   Proceedings of the Third International Symposium ISBMS 2006 on Biomedical Simulation. Editors : Matthias Harders and Gábor Székely.
   preprint

Notes in CRAS

1. Parareal multi-model numerical zoom for parabolic multiscale problems.
   F. Chouly & A. Lozinski. C. R. Math. Vol. 352, Num. 6, pp. 535-540, 2014.
   preprint
2. An added-mass free semi-implicit coupling scheme for fluid-structure interaction.
   M. Astorino, F. Chouly & M.-A. Fernández. C. R. Math. Vol. 347, Num. 1-2, pp. 99-104, 2009.

Book chapters

1. A short perspective on a posteriori error control and adaptive discretizations.
   R. Becker, S.P.A. Bordas, F. Chouly & P. Omnes. Chapter 1 of "Error Control, Adaptive Discretizations, and Applications, Part 1", to appear. Editors : Franz Chouly, Stéphane Pierre Alain Bordas, Roland Becker & Pascal Omnes. Volume 58 of Advances in Applied Mechanics (AAMS). Elsevier.
   preprint
2. Lagrangian and Nitsche methods for frictional contact.
   F. Chouly, P. Hild & Y. Renard. Chapter 1 of "Numerical modeling in highly nonlinear mechanics", to appear. Editors : Jacques Besson, Frédéric Lebon & Eric Lorentz. Wiley/ISTE Editions.
   preprint
3. Méthodes de lagrangien et de Nitsche pour l'approximation numérique des conditions de contact avec frottement.
   F. Chouly, P. Hild & Y. Renard. Chapter 1 of "Modélisation numérique en mécanique fortement non linéaire", pp. 8-52, 2023. Editors : Jacques Besson, Frédéric Lebon & Eric Lorentz. ISTE Editions (Collection Sciences). ISBN 978-1-78948-081-8.
   preprint
4. When a fluid-structure interaction keeps you awake : a physical approach to Obstructive Sleep Apnea.
   A. Van Hirtum, F. Chouly, P.-Y. Lagrée, J.-R. Paoli, Y. Payan & X. Pelorson. Chapter 2 of "Progress in Sleep Apnea Research", pp. 41-76, 2007. Editor : Robert T. Ferber. Nova Science Publishers. ISBN 978-1-60021-652-7.
   preprint

Lecture notes

1. A short journey into the realm of numerical methods for contact in elastodynamics.
   F. Chouly. CEL (Cours en ligne) hal-04204197.
   document
2. Analyse Numérique MIGS 1re Année.
   F. Chouly, X. Dupuis & K. Vuillemot. CEL (Cours en ligne) hal-03277223.
   document
3. An introductive course to some numerical approximation methods for ordinary and partial differential equations.
   F. Chouly. CEL (Cours en ligne) hal-03212748.
   document
4. Sur la prise en compte de quelques conditions aux limites avec la méthode des éléments finis.
   F. Chouly. CEL (Cours en ligne) cel-01564693.
   document

National/international conferences (selection)

1. Schémas HHT-alpha et prédicteurs-correcteurs pour le contact dynamique avec méthode de Nitsche.
   H. Huang, F. Chouly, G. Drouet, N. Pignet. 15e Colloque National en Calcul des Structures, CSMA, 2022.
   preprint
2. In vivo mechanical characterization and tissue-scale modelling of keloid and surrounding healthy skin.
   A. Elouneg, A. Bertin, N. Marie, Q. Lucot, D. Sutula, F. Chouly, A. Lejeune, G. Rolin, T. Lihoreau, B. Chatelain, S.P.A. Bordas, E. Jacquet & J. Chambert. 26th Congress of the European Society of Biomechanics, ESB, 2021.
   preprint
3. Mechanical parameters identification of keloid and surrounding healthy skin using Digital Image Correlation measurements in vivo.
   A. Elouneg, D. Sutula, M. Sensale, F. Chouly, J. Chambert, A. Lejeune, D. Baroli, P. Hauseux, S.P.A. Bordas & E. Jacquet. 24e Congrès Français de Mécanique, CFM, 2019.
   preprint
4. Parameter identification problem in bimaterial human skin and sensitivity analysis: uncertainties in biomechanics of skin.
   D. Sutula, A. Elouneg, M. Sensale, F. Chouly, J. Chambert, A. Lejeune, D. Baroli, P. Hauseux, S.P.A. Bordas & E. Jacquet. 24e Congrès Français de Mécanique, CFM, 2019.
   preprint
5. Generalized local B-bar method for locking phenomenon in Reissner-Mindlin shell and skew-symmetric Nitsche method for boundary conditions imposing and patch coupling in IGA.
   Q. Hu, F. Chouly, A. Zilian, G. Cheng & S.P.A. Bordas. 7th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry, 2017.
   preprint
6. Approximation non biaisée par une méthode de type Nitsche pour le contact en petites et grandes déformations.
   R. Mlika, Y. Renard, F. Chouly. 13e Colloque National en Calcul des Structures, CSMA, 2017.
   preprint
7. Hydro-elastic finite element model of a vocal fold replica.
   N. Hermant, X. Pelorson, P. Luizard, F. Chouly & F. Silva. 22nd International Congress on Sound and Vibration, ICSV, 2015.
   preprint
8. Modèle éléments finis d’un pli vocal artificiel avec couplage hydro-élastique.
   N. Hermant, F. Silva, F. Chouly & X. Pelorson. 12ème Congrès Français d’Acoustique, CFA 2014, pp. 1821-1827 [N°000323], 2014.
   preprint
9. Evaluating soft tissue simulation in maxillofacial surgery using pre and post-operative CT scan.
   M. Chabanas, C. Marécaux, F. Chouly, F. Boutault & Y. Payan. 18th International Conference on Computer Assisted Radiology and Surgery, CARS 2004, ICS, Vol. 1268, pp. 419-424, 2004.
   preprint
10. In-vitro study of pharyngeal pressure losses at the origin of obstructive sleep apnea.
    A. Van Hirtum, F. Chouly, A. Teulé, Y. Payan & X. Pelorson. 25th Annual International Conference of the IEEE Engineering In Medicine And Biology Society, pp. 371-374. 2003.
    preprint

Software and/or data

1. DWR hyperelastic soft tissue.
   M. Duprez, A. Lejeune, F. Chouly, S.P.A. Bordas & H.P. Bui. figshare repository. 2023.
   DOI:10.6084/m9.figshare.22548634.v1
2. Nitsche with a Lagrange Finite Element Method.
   R. Araya & F. Chouly. figshare repository. 2023.
   DOI:10.6084/m9.figshare.24082137.v1
3. Nitsche method for Stokes with slip boundary conditions in FEniCS.
   R. Araya, A. Caiazzo & F. Chouly. figshare repository. 2023.
   DOI:10.6084/m9.figshare.22779443.v1
4. Residual estimator for frictional contact with Nitsche method.
   R. Araya & F. Chouly. figshare repository. 2023.
   DOI:10.6084/m9.figshare.22555573.v1
5. DWR error estimator for the biomechanics of the skin with a keloid scar.
   N. Marie, A. Lejeune, F. Chouly, J. Chambert & E. Jacquet. figshare repository. 2022.
   DOI:10.6084/m9.figshare.19372280.v1
6. Quantifying discretization errors for soft-tissue simulation in computer assisted surgery: a preliminary study.
   M. Duprez, S.P.A. Bordas, M. Bucki, H.P.Bui, F. Chouly, V. Lleras, C. Lobos, A. Lozinski, P.Y. Rohan & S. Tomar. figshare repository. 2019.
   DOI:10.6084/m9.figshare.8128178.v1

Research reports

1. A few remarks about the computer implementation and the verification of some hyperelastic constitutive laws and an illustration with the mechanical response of an artery.
   M. Blaise, F. Chouly & P.Y. Rohan. hal-03637834. 2022.
   report
2. Computing bi-tangents for transmission belts.
   F. Chouly, J. Loubani, A. Lozinski, B. Mejri, K. Merito, S. Passos & A. Pineda. Semaine d'Etude Maths Entreprises (SEME), Besancon, May 2019. hal-02429962. 2020.
   report
3. A stabilised finite element method for a time-dependent problem solved using a fictitious domain method.
   G.R. Barrenechea, F. Chouly & C. Gonzalez. hal-01596106. 2017.
   report
4. Computational fluid dynamics in the upper airway : comparison between different models and experimental data for a simplified geometry with major obstruction.
   F.E. Heravi, M.A. Nazari, F. Chouly, P. Perrier & Y. Payan. hal-01383256. 2016.
   report