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Mathematical Modelling and Scientific Computing

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The research performed by the Mathematical Modelling and Scientific Computing (MMCS) team is concerned with applied mathematics and their interactions, with the following objectives: understanding phenomena by modelling; the mathematical and numerical analysis and the construction of efficient algorithms for computer simulations.

The models which are studied are based on (elliptic, parabolic, hyperbolic, kinetic, dispersive) Partial Differential Equations, variational inequalities, Ordinary Differential Equations, dynamical systems, homogenization theory, multiscale approaches, calculus of variations, geometric measure theory, optimal control, etc. Most of the studies of the team use deterministic models, but others also include stochastic approaches (diffusion limits, regularization by noise).

The numerical methods which are used to approximate solutions are finite differences, finite elements, finite volume methods, discontinuous Galerkin methods, decomposition domain methods, spectral methods. Codes are developped, and at a larger scale parallelization techniques are used. The numerical contributions of the team members both deal with convergence, stability and efficiency issues, and with visualization questions.

The contributions of the team can be divided into three main axes and methodologies, which are non-exclusive since many researchers contribute to several of them: Mathematical modelling for physics and engineering, Mathematical Biology, Numerical methods and Scientific Computing.

Research themes (detailed description)

↓ Mathematical modelling for physics and engineering

The research related to Mathematical modelling for physics and engineering performed in the MMCS team covers a large spectrum of problems: mechanics of structures, fluid mechanices, gas dynamics, and many interaction problems where several states of matter appear. Problems concerned with Image and Discrete Geometry are also studied, with standard physics problems. The contributions with their domains of applications can be presented as follows:

Fluid-structure interactions
Modelling and simulation of lubrification (G. Bayada, M. Boukrouche, S. Ciuperca, M. Jai).
Flows with friction condition (M. Boukrouche, L. Paoli).
Flows in porous media (T. Clopeau, A. Mikelic)
Flows in thin structures and asymptotic expansions (A. Mikelic, G. Panasenko)
Diffusion-absorption (G. Panasenko, V. Volpert).

Non-Newtonian fluids
Polymeric fluids (I. Ciuperca, A. Heibig, L. Palade, A. Zine)
Non-Newtonian aspects for thin films (G. Bayada, M. Boukrouche, L. Paoli)

Analysis and simulations for gas dynamics (A. Boritchev, K. Saleh, J. Vovelle)

Free boundary problems
Surface waves (S. Benzoni-Gavage, F. Chardard, D. Le Roux)
Interfaces and phase transitions (S. Benzoni-Gavage, E. Bretin, E. Canon, T. Clopeau, M. Marion, S. Masnou, A. Mikelic, C. Reichert, J. Vovelle)
Cavitation (G. Bayada, S. Ciuperca, M. Jai)
Geophysics (S. Benzoni-Gavage, F. Chardard, A. Mikelic, G. Panasenko)

Image (E. Bretin, S. Masnou, J.-M. Morvan, M. Picq, J. Pousin, C. Reichert, L. Seppecher)

Discrete geometry (E. Bretin, S. Masnou, J.-M. Morvan)

Properties and mechanics of structures
Contact, deformations and cracking (L. Paoli, A. Petrov, J. Pousin, Y. Renard)
Properties of structures (E. Bretin, E. Fouassier, L. Seppecher, G. Vial, A. Zine)
Materials with form memory (L. Paoli, A. Petrov)
Composite models (E. Canon, I. Ciuperca, M. Jai, I. Kostin, G. Panasenko)

↓ Mathematical Biology

The research on mathematical biology made by the MMCS team is strongly motivated by modelling. There are many collaborations with biologists and medical researchers, and a large spectrum of theoretical tools is covered. There are several natural links with the other research axes of the team. A substantial part of the mathematical biology research is associated with the Inria Dracula team.

Blood modelling
Blood flow (N. Debit, G. Panasenko, M.C. Viallon, V. Volpert, A. Zine)
Atherosclerosis modelling (V. Volpert, A. Zine)
Erythropoiesis (F. Crauste, L. Pujo-Menjouet, V. Volpert)

Dynamical phenomena
Cellular renewal (M. Adimy, S. Bernard, F. Crauste, T. Dumont, P. Michel)
Prion dynamics (I. Ciuperca, L. Palade, L. Pujo-Menjouet)
Population dynamics (T. Lepoutre, M. Marion, J. Pousin, V. Volpert)
Reproduction (P. Michel)

↓ Numerical methods and Scientific Computing

The analysis and development of numerical methods, as well as developping efficient codes, belong to the traditional research axes of the MMCS team. This theme is separated from the others due to the diversity of tools, however most of the works are associated with modelling studies.

Finite volume methods : schemes for the simulation of flows (Navier-Stokes, Euler, Baer-Nunziato, shallow waters) or diffusion equations (with coupling between domains of different dimensions) (S. Delcourte, D. Le Roux, M. Marion, G. Panasenko, K. Saleh, M.-C. Viallon)

Galerkin methods : schemes for the simulation of contact, multi-cracking, plastic deformation phenomena, for the simulation of shallow water folows, for heterogeneous coupling of Darcy-Stokes type, for the propagation of elastic, acoustic or electromagnetic waves, adaptive schemes (A. Agouzal, M. Bergot, N. Debit, S. Delcourte, D. Le Roux, A. Petrov, Y. Renard)

Spectral methods
Spectral theory (M. Ahues Blanchait, L. Grammont, D. Le Roux)
RKHS (Reproducing Kernel Hilbert Spaces) theory and applications to nuclear safety (M. Ahues Blanchait, L. Grammont)

High-performance computing and Numerical linear algebra
Domain decomposition, system decoupling and applications to the simulation of the Darcy law in 3D with strongly heterogeneous permeability (D. Tromeur-Dervout)
Conditioning, applications to the approximate resolution of differential, albegraic or integral equations (M. Ahues Blanchait, D. Tromeur-Dervout)
Stiff reaction-diffusion systems and applications to cardiac surgery and combustion (T. Dumont)

Numerical methods for integral equations and applications to the study of interstella radiative transfert (M. Ahues Blanchait, L. Grammont)


  • The Mathematical Modelling and Scientific Computing Seminar is common to ICJ and UMPA. It is co-organizd by E. Bretin (ICJ, INSA Lyon), V. Calvez (UMPA, ENS Lyon), K. Saleh (ICJ, Lyon 1) and P. Vigneaux (UMPA, ENS Lyon). It takes place every two weeks, on Tuesdays at, at Lyon 1 or ENS Lyon, alternatively.
  • Seminars Biomathématiques are organized by the Dracula Inria team; they generally take place on Thursdays at in the CEI building, la Doua Campus.
  • The working seminar Numerical methods for science and engineering is co-organized by A. Petrov (INSA Lyon) and G. Vial (Centrale Lyon), it takes place at INSA de Lyon or at École Centrale de Lyon.


 Mostafa Adimy   +33 (0)472448526   (UCBL-Braconnier  256)    
 Abdellatif Agouzal   +33 (0)472431629   (UCBL-Braconnier  104)    
 Mario Paul Ahues Blanchait   +33 (0)477421776   (UJM-Metare  MU 613)    
 Sylvain Arguillère   +33 (0)472447938   (UCBL-Braconnier  247)    
 Alexis Auvray   +33 (0)472186534   (ECL-E6  6216)    
 Guy Bayada   +33 (0)472438312   (INSA-Vinci  135)    
 Sylvie Benzoni-Gavage   +33 (0)472448502   (UCBL-Braconnier  241)    
 Morgane Bergot   +33 (0)472431690   (UCBL-Braconnier  228)    
 Samuel Bernard   +33 (0)472448317   (UCBL-Braconnier  248)    
 Apollos Besse   +33 (0)472437492   (INRIA-CEI2  423 (INRIA))    
 Olivier Bodart   +33 (0)477481531   (UJM-Metare  B 102)    
 Alexandre Boritchev   +33 (0)472446248   (UCBL-Braconnier  124)    
 Anass Bouchnita   +33 (0)472431374   (UCBL-Braconnier  100)    
 Mahdi Boukrouche   +33 (0)477481535   (UJM-Metare  C 104)    
 Loïs Boullu   +33 (0)472431374   (UCBL-Braconnier  100)    
 Elie Bretin   +33 (0)472438310   (INSA-Vinci  132)    
 Nils Caillerie   +33 (0)472431374   (UCBL-Braconnier  100)    
 Vincent Calvez   +33 (0)472431357   (UCBL-Braconnier  253)    
 Aurelien Canet   +33 (0)472447912   (INSA-CEI1  ...)    
 Eric Canon   +33 (0)477485103   (UJM-Metare  B 108)    
 Marie-Claude Canon-Viallon   +33 (0)477481533   (UJM-Metare  B 101A)    
 Sylvie Champier   +33 (0)477481501   (UJM-Metare  C 132)    
 Frédéric Chardard   +33 (0)477481538   (UJM-Metare  B 101B)    
 Abdennasser Chekroun   +33 (0)472437513   (INSA-CEI1  26)    
 Ionel Ciuperca   +33 (0)472431008   (UCBL-Braconnier  246)    
 Thierry Clopeau   +33 (0)472448515   (UCBL-Braconnier  251)    
 Fabien Crauste   +33 (0)472448516   (UCBL-Braconnier  252)    
 Farshid Dabaghi   +33 (0)477481546   (UJM-Metare  Bureau des doctorants)    
 Naima Débit   +33 (0)472431089   (UCBL-Braconnier  241)    
 Sarah Delcourte   +33 (0)472431186   (UCBL-Braconnier  207)    
 Thierry Dumont   +33 (0)472448523   (UCBL-Braconnier  257)    
 Arnaud Duran   +33 (0)472448207   (UCBL-Braconnier  242)    
 Elise Fouassier   +33 (0)472448052   (UCBL-Braconnier  254)    
 Tatiana Galochkina   +33 (0)472431374   (UCBL-Braconnier  100)    
 Pierre-Marie Gibert   +33 (0)4724.....   (Polytech  ...)    
 Olivier Gipouloux   +33 (0)477481534   (UJM-Metare  C 106)    
 Simon Girel   +33 (0)472437489   (INSA-CEI1  5)    
 Laurence Grammont   +33 (0)477481534   (UJM-Metare  C 106)    
 Arnaud Heibig   +33 (0)472438288   (INSA-Vinci  134)    
 Maxime Herda   +33 (0)472431190   (UCBL-Braconnier  219)    
 Mohammed Jai   +33 (0)472438311   (INSA-Vinci  136)    
 Ilya Kostin   +33 (0)477481552   (UJM-Metare  C104)    
 Frédéric Lagoutière   +33 (0)472431334   (UCBL-Braconnier  222)    
 Daniel Le Roux   +33 (0)472446280   (UCBL-Braconnier  103 bis)    
 Thomas Lepoutre   +33 (0)472448317   (UCBL-Braconnier  248)    
 Jean-François Maitre   +33 (0)472186445   (ECL-E6  6231)    
 Martine Marion   +33 (0)472186446   (ECL-E6  6230)    
 Simon Masnou   +33 (0)472431386   (UCBL-Braconnier  253)    
 Philippe Michel   +33 (0)472186084   (ECL-E6  6209)    
 Andro Mikelic   +33 (0)426234548   (UCBL-Braconnier  119)    
 Jean-Marie Morvan   +33 (0)472431252   (UCBL-Braconnier  225)    
 François Musy   +33 (0)472186448   (ECL-E6  6224)    
 Fabienne Oudin-Dardun   +33 (0)472432766   (UCBL-Istil  )    
 Liviu Palade   +33 (0)472438916   (INSA-Vinci  138)    
 Grigory Panasenko   +33 (0)477481542   (UJM-Metare  B 109)    
 Laëtitia Paoli   +33 (0)477485112   (UJM-Metare  C 103)    
 Adrien Petrov   +33 (0)472438837   (INSA-Vinci  133)    
 Martine Picq   +33 (0)472438168   (INSA-Vinci  131)    
 Jérôme Pousin   +33 (0)472438836   (INSA-Vinci  131)    
 Laurent Pujo-Menjouet   +33 (0)472431008   (UCBL-Braconnier  246)    
 Christian Reichert   +33 (0)472438310   (INSA-Vinci  132)    
 Yves Renard   +33 (0)472438708   (INSA-Vinci  08C)    
 Emmanuel Risler   +33 (0)472438021   (INSA-Vinci  RDC 401 0 08B)    
 Philippe Saadé   +33 (0)472448525   (UCBL-Braconnier  255)    
 Khaled Saleh   +33 (0)472448207   (UCBL-Braconnier  242)    
 Dominique Sandri   +33 (0)472448516   (UCBL-Braconnier  252)    
 Laurent Seppecher   +33 (0)472186444   (ECL-E6  6233)    
 Nicolae Razvan Stoica   +33 (0)4   (INSA-Pascal  502-415)    
 Benjamin Texier   +33 (0)472448516   (UCBL-Braconnier  252)    
 Léon Tine   +33 (0)472448515   (UCBL-Braconnier  251)    
 Damien Tromeur-Dervout   +33 (0)472431356   (UCBL-Istil  CDCSP/ISTIL)    
 Grégory Vial   +33 (0)472186790   (ECL-E6  6203)    
 Vitaly Volpert   +33 (0)472432765   (UCBL-Braconnier  249)    
 Julien Vovelle   +33 (0)472447949   (UCBL-Braconnier  258)    
 Abdel Malek Zine   +33 (0)472186458   (ECL-E6  6223)    

Nombre de personnes : 75


Head of the team: Simon Masnou
Webmaster: Simon Masnou