Membres

Travaux récents

Optimized hybrid materials

Anhydrous salts are the most commonly used Phase Change Materials (PCMs) in thermal energy storage (TES) applications at high temperature. Like most PCM, salts,
due to their low thermal conductivity (typically < 1W/m/K),
impose heat transfer limitations that can lead to over-sized heat exchangers. Different techniques for heat transfer enhancement have been proposed in the past. The most efficient ones are those in which a conductive porous structure is saturated with the salt, thus leading to composite materials with increased effective thermal conductivity.
The objective is to improve Thermal Energie Storage composite materials by acting on the shape of the carrier material structure. Tools and algorithms based essentially on geometrical and topological shape optimization approaches are under developement.
PCM composite materials are often characterized by :
 high contrast between the thermal properties of the phases,
 small granularity, complex geometry of the interface separating the phases, and
 temperature jumps at the interface due to thermal contact resistances.
These specific characteristics lead to some numerical difficulties that must be handled efficiently. Hybrid Dual Raviart–Thomas Finite Elements, is then proposed to solve the direct enthalpy equation.

Publications

• Two Phases Stefan Problem with Smoothed Enthalpy. Accepted for publication in Communication in Mathematical Sciences, 2016. (co-authored with M. Azaïez, J. Shen).

• Finite Element Methods for the Temperature in Composite Media with Contact Resistance, Journal of Scientific Computing, 63, 478-501, 2015. (co-authored with C. Bernardi, F. Ben Belgacem, M. Mint Brahim).

• A substructuring method for phase change modelling in hybrid media. Computers & Fluids, 88, 81-92, 2013.(co-authored with M. Azaïez, E. Palomo Del Barrio).

Regularization methods for data completion problem & source detection

The major contribution in this topic, involves providing a new regularization issues of the ill-posed Cauchy problem for the Laplace equation. Extend the domain from the incomplete data side, then replace it by a fictitious ( regular) boundary, lead to more precise and regular solution in the original domain.

Publications

• Uniqueness’ failure for the finite element Cauchy-Poisson’s problem. Comput. Math. Appl. 135 (2023), 77–92. (Co-authored with F. Ben Belgacem, V. Girault).

• Full discretization of Cauchy’s problem by Lavrentiev-finite element method. SIAM J. Numer. Anal. 60 (2022), no. 2, 558–584. (Co-authored with F. Ben Belgacem, V. Girault).

• Analysis of Lavrentiev-Finite Element Methods for Data Completion Problems. Numerische Mathematik, 139, 1-25, 2018
  Volume 139 Issue 1, 2018. (Co-authored with F. Ben Belgacem, V. Girault).

• Local Convergence of the Lavrentiev Method for the Cauchy Problem via a Carleman Inequality. Journal of Scientific Computing,53, 320-341, 2012. (Co-authored with F. Ben Belgacem, T. D. Du ).

• Extended-domain-Lavrentiev’s regularization for the Cauchy problem, Inverse problems, 27, 2011. (Co-authored with F. Ben Belgacem, T. D. Du ).

• The density function reconstruction of surface sources from a single Cauchy measurement, Computers & Fluids, 43, 14-22, 2011. (Co-authored with M. Azaïez, F. Ben Belgacem).

• A finite element model for the data completion problem : analysis and assessment. Inverse Problems in Science and
  Engineering, 19, 1063-1086, 2011. (Co-authored with M. Azaïez, F. Ben Belgacem, T. D. Du ).

• A preconditioned Richardson regularization for the data
  completion problem and the Kozlov-Maz’ya-Fomin method. Revue ARIMA, 13, 17-32, 2010. (Co-authored with T. D. Du)

• Identifiability of Surface Sources from a Cauchy Data. Inverse Problems, 25, 075007, 14 pp, 2009. (Co-authored with F. Ben Belgacem).

• The Lavrentiev Regularization for the Data Completion Problem. Inverse Problems, 24, 045009 14 pp. 2008. (Co-authored with F. Ben Belgacem, H. El Fekih).

• Parameter choice in the Lavrentiev regularization of the data completion problem. Journal of Physics : 135-012016, 9 pp. 2008. (Co-authored with F. Ben Belgacem, H. El Fekih).

Total overlapping Schwarz Method for elliptic problems

In this theme, two major applications have been destined to our variant of total overlapping Schwarz method.
The first one, concerns the approximation of the absorbing boundary condition, in unbounded domains. That same method
turns to be an efficient tool to make numerical zooms in regions of a particular interest.

Publications

• On the Schwarz method for the eddy currents model. Comput. Math. Appl. 113 (2022), 174–188. (Co-authored with N. Gmati, M, Anis).

• Computational zooming in near unilateral cracks by Schwarz method with total overlap. J. Math. Study 52 (2019), no. 4, 378–393. (Co-authored with F. Ben Belgacem, N. Gmati).

• Total overlapping Schwarz’ preconditioners for elliptic problems. Modélisation mathématique et analyse num´erique, 45, 91-113, 2011. (Co-authored with F. Ben Belgacem, N. Gmati).

• Convergence Bounds of GMRES with Schwarz’
  Preconditioner for the Scattering Problem. International Journal for Numerical Methods in Engineering, 80, 191 − 209, 2009. (Co-authored with F. Ben Belgacem, N. Gmati).

• Calcul des courants de Foucault harmoniques dans des domaines non bornés par un algorithme de point fixe de Cauchy. Paru dans Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées (ARIMA), 5, pp. 168-182, 2006.

• On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems. M2AN, Model. Math. Anal. Numer,
  39, 693-714, 2005. (Co-authored with F. Ben Belgacem, N. Gmati).

• Sur le traitement des conditions aux limites à l’infini pour quelques problèmes extérieurs par la méthode de Schwarz Alternée. C. R. Acad. Sci. Paris, 333, Série I, 277-282, 2003. (Co-authored with F. Ben Belgacem, M. Fournié, N. Gmati).