11 citations · 39 across the 8 of their papers we have counts for
8 papers
Microscopic tridomain model of electrical activity in the heart with dynamical gap junctions. Part 2 -- Derivation of the macroscopic tridomain model by unfolding homogenization method
Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad +1
We study the homogenization of a novel microscopic tridomain system, allowing for a more detailed analysis of the properties of cardiac conduction than the classical bidomain and m…
Microscopic Tridomain Model of Electrical Activity in the Heart with Dynamical Gap Junctions. Part 1 -- Modeling and Well-Posedness
Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad +1
We present a novel microscopic tridomain model describing the electrical activity in cardiac tissue with dynamical gap junctions. The microscopic tridomain system consists of three…
Three Scale Unfolding Homogenization Method Applied to Cardiac Bidomain Model
Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad +1
In this paper, we are dealing with a rigorous homogenization result at two different levels for the bidomain model of cardiac electro-physiology. The first level associated with th…
Derivation of a new macroscopic bidomain model including three scales for the electrical activity of cardiac tissue
Fakhrielddine Bader, Mostafa Bendahmane, Mazen Saad +1
In the present paper, a new three-scale asymptotic homogenization method is proposed to study the electrical behavior of the cardiac tissue structure with multiple heterogeneities…
A combined finite volume--nonconforming finite element scheme for compressible two phase flow in porous media
Bilal Saad, Mazen Saad
We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion te…
Study of full implicit petroleum engineering finite volume scheme for compressible two phase flow in porous media
Bilal Saad, Mazen Saad
An industrial scheme, to simulate the two compressible phase flow in porous media, consists in a finite volume method together with a phase-by-phase upstream scheme. The implicit f…
Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository
Florian Caro, Bilal Saad, Mazen Saad
Our goal is the mathematical analysis of a two phase (liquid and gas) two components (water and hydrogen) system modeling the hydrogen displacement in a storage site for radioactiv…
Convergence of a Finite Volume Scheme for Gas Water Flow in a Multi-Dimensional Porous Media
Mostafa Bendahmane, Ziad Khalil, Mazen Saad
A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volu…