Toufic El Arwadi

Toufic El Arwadi
Faculty: ScienceDepartment: Mathematics & Computer SciencePosition: Associate Professor of Pure MathematicsOffice Number: B114 (A3 building)Phone: +961 7 985 858Ext: 3320E-mail: t.elarwadi@bau.edu.lb

Biography

Dr El Arwadi has completed his PhD in Mathematical Analysis from University of Poitiers in 2010. He worked (as TA) at the department of Mathematics of university of Paris 13 and University of Aix-Marseille. Currently, he is an associate professor of Mathematics  at Beirut Arab University since 2016. He is a mathematician mainly interested in inverse problems of medical imaging and semigroup theory. The goal of his scientific work is to design efficient numerical methods that have a sound mathematical basis. He have published research articles mostly about the following topics: Electrical Impedance Tomography (EIT), Inverse conductivity problem, elliptic and parabolic problem with dynamical boundary conditions.

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Teaching

Previous courses

Undergraduate Courses:

Set theory, Probability , Statistics, Numerical analysis, Linear algebra, Discrete mathematics , Mathematical analysis, Operations research, Differential Geometry, Topology, Advanced Numerical Analysis, Measure theory

Graduate Courses:

Research topic, Advanced numerical analysis, The finite element method, Numerical linear algebra, Distributions Theory, Evolution Equations, Spectral theory, Measure and Integration, Advanced Analysis and Applications.

Spring 2015/2016

Research

Research Interests

Inverse Problems: Studying the D-bar method : Establishing error estimates for the regularisation and effect of the geometry.  
Establishing stability estimates for regularisation.

Semigroups: Theoretical approximation for the Dirichlet-to-Neumann semigroup by using Chernoff procedure.  Numerical scheme for solving elliptic and parabolic linear problem with dynamical boundary conditions.

Publications

1. T. El Arwadi Méthode De Dbar Pour La Résolution Du Problème De Conductivité, Nouvelle Approche ( Europian University Edition)

2. T. El Arwadi Error estimates for reconstructed conductivities via the D-bar method. Numerical Functional Analysis and Optimization ,Vol. 33, Iss. 1, 2012 ,pp 21-38

3. M.A. Cherif and T. El Arwadi . D-Bar Method for Smooth and Nonsmooth Conductivities .Vol. 35, Iss. 2, 2014 ,pp 198-222

4. M.A. Cherif, T. El Arwadi, H. Emamirad, J.M Sac Épée The Dirichlet-to-Neumann semigroup acts as a magnifying glass Semigroup Forum, Vol. 88, Iss. 3, 2014 ,pp 753-767

5. R. Ahmad, T. El Arwadi, H. Chrayteh, J.M Sac Épée A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup J. App. Math, Vol. 2015, Article ID 429641, http : dx.doi.org/10.1155/2015/429641

6. T. El Arwadi, S. Dib, T. Sayah A Priori and A Posteriori error estimates for an elleptic problem with dynamical boundary conditions App. Math. Inf. Sc., 6 (9), DOI :10.12785/amis/100121 (2015) pp 2205-2217

7. T. El Arwadi, A. Zaart A Novel 5x5 Edge Detection Operator for Blood Vessel Images British Journal of Applied Science and Technology 11(3) :1-10, 2015, Article no.BJAST.19967 ISSN : 2231-0843

8. A. Zaart, T. El Arwadi A New Edge Detection Method for CT-Scan Lung Images Journal Of Biomedical Engineering And Medical Imaging 2(5), ISSN :2055-1266, DOI : 10.14738/jbemi.25.1453

9. T. El Arwadi, T. Sayyah Lp estimates for Dirichlet-to-Neumann operator and applications EJDE, Vol. 2015, No. 258 pp 1-8, ISSN : 1072-6691

10. R. Ahmad, T. El Arwadi, H. Chrayteh, J.M Sac Épée A Priori and A Posteriori Error Estimates for a Crank Nicolson Type Scheme of an Elliptic Problem with Dynamical Boundary Conditions J. Math. Res., Vol 8, No 2 (2016), http ://dx.doi.org/10.5539/jmr.v8n2p1

11. S. Al Kontar, T. El Arwadi, H. Chrayteh, J.M Sac Épée Stability of the D-bar reconstruction method for complex conductivities The Australian Journal of Mathematical Analysis and Applications Vol. 13, No 1, pp :1-14 (2016)

12. T. El Arwadi, V. Flammang, G.Rhin, J.M Sac Épée Extension of the notion of Mahler measure to a certain class of holomorphic functions. Properties and applications. Results in Math 72, no. 1-2, 787-791 (2017)

13. S. Al Kontar, T. El Arwadi, H. Chrayteh, J.M Sac Épée About the D-Bar reconstruction method for complex conductivities : Error estimates (To appear)

14. T. El Arwadi, A. Wehbe, W. Youssef Theoretical and Numerical observability of the Bresse Beam (Submitted)

Activities

- I organized a workshop on Partial differential equations 2015 (Day of Partial Differential Equations).

-  2012 - LSMS annual meeting (member of the scientific committee).

- 2013 - LSMS annual meeting (member of the organizing committee).

- 2014 - LSMS annual meeting (member of the organizing committee).

- 2014 - LAAS annual Workshop (member of the scientific committee).

- 2015- LSMS annual meeting (member of the organizing committee).

- 2015 - LAAS annual Workshop (member of the scientific committee).

- 2016- LSMS annual meeting (member of the organizing committee).

- 2016 - LAAS annual Workshop (member of the scientific committee).

Recent Oral Presentations


- 12/2012 LSMS meeting New approach of D-bar methods

- 07/2012 9th AIMS workshop (Orlando) New approach of D-bar methods

- 12/2012 Lebanese University - Fanar New approach of D-bar methods

- 09/2013 Saint-Joseph University On the Dirichlet-to-Neumann semigroup

- 07/2015 Saint-Joseph University The electrical impedance tomography and inverse problems

- 10/2016 Université Badji Mokhtar Annaba New approach of D-bar method for EIT and inverse convection problem

- 03/2016 Lebanese University – Hadath  Electrical impedance tomography and D-bar method.

- Curriculum committee, member.

- Comprehensive exam committee, member

- Students Activities committee, member.

- Graduate seminar in Mathematics and Computer sciences, organizer

- 2012 -2015 Lebanese Society for the Mathematical Sciences (National Relations)

- 2015- Lebanese Society for the Mathematical Sciences (International Relations)

International Collaborators


- A. Tamasan (UCF, Florida, USA)

- M.A Cherif (University of Sfax, Tunisia)

- M. Uesaka (University of Tokyo, Japan)

- H. Emamirad (University of Poitiers, France)

- J.M Sac-Epée (Lorraine university, France)