7 citations · 7 across the 11 of their papers we have counts for
12 papers
Numerical study of a diffusion equation with Ventcel boundary condition using curved meshes
Fabien Caubet, Joyce Ghantous, Charles Pierre
In this work is provided a numerical study of a diffusion problem involving a second order term on the domain boundary (the Laplace-Beltrami operator) referred to as the \textit{Ve…
Analytical properties of Graetz modes in parallel and concentric configurations
Charles Pierre, Franck Plouraboué
The generalized Graetz problem refers to stationary convection-diffusion in uni-directional flows. In this contribution we demonstrate the ana-lyticity of generalized Graetz soluti…
Exponential Adams Bashforth integrators for stiff ODEs, application to cardiac electrophysiology
Yves Coudière, Charlie Douanla Lontsi, Charles Pierre
Models in cardiac electrophysiology are coupled systems of reaction diffusion PDE and of ODE. The ODE system displays a very stiff behavior. It is non linear and its upgrade at eac…
Approximation of the Ventcel problem, numerical results
Charles Pierre, Marc Dambrine
Report on the numerical approximation of the Ventcel problem. The Ventcel problem is a 3D eigenvalue problem involving a surface differential operator on the domain boundary: the L…
Efficient high order schemes for stiff ODEs in cardiac electrophysiology
Charlie Douanla Lontsi, Yves Coudière, Charles Pierre
In this work we analyze the resort to high order exponential solvers for stiff ODEs in the context of cardiac electrophysiology modeling. The exponential Adams-Bashforth and the Ru…
Raviart Thomas Petrov-Galerkin Finite Elements
François Dubois, Isabelle Greff, Charles Pierre
The general theory of Babuška ensures necessary and sufficient conditions for a mixed problem in classical or Petrov-Galerkin form to be well posed in the sense of Hadamard. Moreov…
Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology
Yves Coudière, Charlie Douanla Lontsi, Charles Pierre
To address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly…
Preconditioning the bidomain model with almost linear complexity
Charles Pierre
The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic react…
Raviart-Thomas finite elements of Petrov-Galerkin type
François Dubois, Isabelle Greff, Charles Pierre
The mixed finite element method for the Poisson problem with the Raviart-Thomas elements of low-level can be interpreted as a finite volume method with a non-local gradient. In thi…
Analysis of time-stepping methods for the monodomain model
Thomas Roy, Yves Bourgault, Charles Pierre
To a large extent, the stiffness of the bidomain and monodomain models depends on the choice of the ionic model, which varies in terms of complexity and realism. In this paper, we…
Discrete embeddings for Lagrangian and Hamiltonian systems
Jacky Cresson, Isabelle Greff, Charles Pierre
The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with…
Convergence of discrete duality finite volume schemes for the cardiac bidomain model
Boris Andreianov, Mostafa Bendahmane, Kenneth H. Karlsen +1
We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the he…