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Charles PIERRE
 CNRS engineer-researcher in applied mathematics
Université de Pau et des Pays de l'Adour





Address:

Laboratoires de Mathématiques et de leurs Applications de Pau

Université de Pau et des Pays de l'Adour

Pau - FRANCE

011-33 (0)5-59-40-75-27




Topics
Students
Participation à des projets de recherche
Some presentations
Journal Papers
  1. Charles Pierre, Guy Vallet.
    A mathematical model of marine mucilage, the case of the liga on the Basque coast.
    Mathematical Modelling of Natural Phenomena, 18: 2023.

  2. Thomas Roy, Yves Bourgault and Charles Pierre.
    Analysis of time-stepping methods for the monodomain model.
    Computational and Applied Mathematics, 39(8): 2020.

  3. Yves Coudière, Charlie Douanla-Lontsi and Charles Pierre.
    Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology.
    Electronic Transactions on Numerical Analysis, 52: 342-357, 2020.

  4. Charles Pierre and Franck Plouraboué.
    Analytical properties of Graetz modes in parallel and concentric configurations.
    Meccanica, 55(8): 1545 - 1559, 2020.

  5. Francois Dubois, Isabelle Greff and Charles Pierre.
    Raviart-Thomas finite elements of Petrov-Galerkin type.
    M2AN 53(3): 1553 - 1576, 2019.

  6. Yves Coudière, Charlie Douanla-Lontsi and Charles Pierre.
    Exponential Adams Bashforth integrators for stiff ODEs, application to cardiac electrophysiology.
    Mathematics and Computers in Simulation, 153: 15-34, 2018.

  7. Jacky Cresson, Isabelle Greff and Charles Pierre.
    Discrete embeddings for Lagrangian and Hamiltonian systems.
    Acta Mathematica Vietnamica, 43(3): 391-413, 2018.

  8. Yves Coudière, Charlie Douanla-Lontsi and Charles Pierre.
    Efficient high order schemes for stiff ODEs in cardiac electrophysiology.
    ARIMA, 28: 1-12, 2017.

  9. Charles Pierre, Julien Bouyssier, Frédéric de Gournay and Franck Plouraboué.
    Numerical computation of 3D heat transfer in complex parallel convective exchangers using generalized Graetz modes.
    Journal of Computational Physics, 268: 84-105, 2014

  10. Julien Bouyssier, Charles Pierre and Franck Plouraboué.
    Mathematical analysis of parallel convective exchangers with general lateral boundary conditions using generalised Graetz modes.
    M3AS, 24(4): 627-665, 2014.

  11. Jérome Fehrenbach, Frédéric de Gournay, Charles Pierre and Franck Plouraboué.
    The Generalized Graetz problem in finite domains.
    SIAM Journal on Applied Mathematics, 72(1): 99-123, 2012.

  12. Charles Pierre.
    Preconditioning the bidomain model with almost linear complexity.
    Journal of Computational Physics, 231(1): 82-97, 2012.

  13. Boris Andreianov, Nostafa Bendahmane, Kenneth Karlsen and Charles Pierre.
    Convergence of discrete duality finite volume schemes for the cardiac bidomain model.
    Networks and Heterogeneous Media, 6(2): 195-240., 2011.

  14. Charles Pierre and Franck Plouraboué.
    Numerical analysis of a new mixed-formulation for eigenvalue convection-diffusion problems.
    SIAM Journal on Applied Mathematics, 70(3): 658-676, 2009.

  15. Yves Coudière, Charles Pierre, Olivier Rousseau and Rodolphe Turpault.
    A 2D/3D discrete duality finite volume scheme, application to ECG simulation.
    International Journal on Finite Volumes, 6(1), 2009.

  16. Yves Bourgault, Yves Coudière and Charles Pierre.
    Existence and uniqueness of the solution for the bidomain model used in cardiac electrophysiology.
    Nonlinear Analysis: Real World Applications, 10(1): 458-482, 2009.

  17. Franck Plouraboué and Charles Pierre.
    Stationary convection-diffusion between two co-axial cylinders.
    International Journal of Heat and Mass Transfer, 50(23-24): 4901-4907, 2007.

  18. Yves Coudière and Charles Pierre.
    Stability and convergence of a finite volume method for two systems of reaction-diffusion equations in electro-cardiology.
    Nonlinear Analysis: Real World Applications, 7(4): 916-935, 2006.

  19. Charles Pierre, Franck Plouraboué and Michel Quintard.
    Convergence of the Generalized Volume Averaging Method on a Convection-Diffusion Problem: A Spectral Perspective.
    SIAM Journal on Applied Mathematics, 66(1): 122-152, 2005.

Conference proceedings
  1. Fabien Caubet, Joyce Ghantous and Charles Pierre.
    Numerical analysis of a diffusion equation with Ventcel boundary condition using curved meshes.
    Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications, Jaca, 2022.
    pp 63-73.

  2. Francois Dubois, Isabelle Greff and Charles Pierre.
    Raviart-Thomas Petrov--Galerkin finite elements.
    International Conference on Finite Volumes for Complex Applications VIII, Lille, 2018.
    Methods and Theoretical Aspects, pp 341-349.

  3. Yves Coudière, Charlie Douanla-Lontsi and Charles Pierre.
    Efficient high order schemes for stiff ODEs in cardiac electrophysiology.
    African Conference on Research in Computer Sciences and Applied Mathematics. Tunis, 2016.

  4. M Pop, M Sermesant, T Mansi, E Crystal, S Ghate, J Relan, C Pierre, Y Coudière, J Barry, I Lashevsky, B Qiang, ER McVeigh, N Ayache, GA Wright.
    EP challenge - STACOM'11: forward approaches to computational electrophysiology using MRI- based models and in-vivo CARTO mapping in swine hearts.
    2nd international workshop STACOM, Toronto, 2011. Lecture Notes in Computer Science (Springer) 7085: 1-13.

  5. Yves Coudière and Charles Pierre.
    Benchmark 3D: CeVe-DDFV, a discrete duality scheme with cell/vertex unknowns.
    International Conference on Finite Volumes for Complex Applications VI, Praha, 2011.

  6. Yves Coudière, Charles Pierre, Rodolphe Turpault.
    A 2D/3D Finite Volume Method used to solve the bidomain equations of electrocardiology.
    ALGORITHMY 2009. 18th Conference on Scientific Computing, Slovakia, 2009.

  7. Yves Coudière, Charles Pierre, Olivier Rousseau and Rodolphe Turpault.
    2D/3D Discrete Duality Finite Volume (DDFV) scheme for anisotropic- heterogeneous elliptic equations, application to the electrocardiogram simulation.
    International Conference on Finite Volumes for Complex Applications V, Aussois (France), 2008.

  8. Yves Coudière and Charles Pierre.
    Stability and Convergence of a Finite Volume Method for a Reaction Diffusion System in Electro-Cardiology.
    International Conference on Finite Volumes for Complex Applications IV, Marrakech, 2005.

Other
  1. Fabien Caubet, Joyce Ghantous and Charles Pierre.
    A priori error estimates of a diusion equation with Ventcel boundary conditions on curved meshes
    Preprint, hal-04144655, 2023.

  2. Fabien Caubet, Joyce Ghantous and Charles Pierre.
    Numerical study of a diffusion equation with Ventcel boundary condition using curved meshes.
    Preprint, hal-03972051, 2023.

  3. Charles Pierre.
    Approximation of the Ventcel problem, first numerical results.
    HAL report, hal-00985720, 2014.

  4. Charles Pierre and Yves Bourgault.
    A comparison of the Bidomain and the adapted monodomain models in electro-cardiology.
    HAL report, hal-00545888v1, 2010.

  5. Charles Pierre.
    Modelling and simulating the electrical activity of the Heart embedded in the torso, numerical analysis and finite volumes methods.
    PhD Thesis, Université de Nantes, 2005.

CUMIN
Curved Meshes In Numerical simulations

CUMIN is a finite element library including

  • finite elements of order >= 1,
  • curved geometries: meshes of geometrical degrree >= \f$ 1,
  • solvers for diffusion and linear elasticity PDEs,
  • coupling with linear system solvers and eigenvalue problem solvers,
  • Language: modern Fortran,
  • Link to gitlab deposit ,
  • API documentation .
CHORAL
Cardiac-electrophysiology High-Order Algorithms

A Fortran 2003 code for parabolic reaction-diffusion equations

Applications to electro-physiology

Download


Brief description
Features:
  • High order stabilized time-stepping methods for stiff problems
    (exponential integrators, ImEx and operator splitting methods).
  • High-order finite element methods.
  • High-order curved geometry
    (parametric elements).
Applications:
  • Evolution reaction-diffusion equations coupled with ODE systems,
    (ionic models for cellular action potential, monodomain model, anisotropic tissues ).
  • Elliptic equations.
Dependencies:
  • Fortran compiler.
  • Mesh generation and visualization based on Gmsh.
Gallery


     
Short Vitæ
2007  :   CNRS Research Engineer
Laboratoires de Mathématiques et de leurs Applications - PAU
Université de Pau et des Pays de l'Adour.

2005-2007  : CRM Postdoctoral Fellowship, with Y. Bourgault
Department of Mathematics and Statistic,
University of Ottawa.

2002-2005  : PhD in Applied Mathematics, with Y. Coudière and F. Jauberteau.
Laboratoire de Mathématiques Jean Leray ,
Université de Nantes.

2001-2002  : Master in Applied Mathematics (Université de Nantes),
Master Thesis with F. Plouraboué
at the IMFT (Institut de Mécanique des Fluides de Toulouse).