Toufic-El Arwadi

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Toufic El Arwadi
Professor of Mathematics

Mathematics & Computer Science

Toufic El Arwadi

Professor of Mathematics

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 a full professor of Mathematics at Beirut Arab University since 2016. He is a mathematician mainly interested in inverse problems of medical imaging and control theory. The goal of his scientific work is to design efficient numerical methods that have a sound mathematical basis. He has published research articles mostly about the following topics: Electrical Impedance Tomography (EIT), Inverse conductivity problem, elliptic and parabolic problem with dynamical boundary conditions, Bresse and Timoshenko-type systems.
 

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 a full professor of Mathematics at Beirut Arab University since 2016. He is a mathematician mainly interested in inverse problems of medical imaging and control theory. The goal of his scientific work is to design efficient numerical methods that have a sound mathematical basis. He has published research articles mostly about the following topics: Electrical Impedance Tomography (EIT), Inverse conductivity problem, elliptic and parabolic problem with dynamical boundary conditions, Bresse and Timoshenko-type systems.
 

Fall 2015/2016:

  • Mathematical Analysis II
  • Linear Algebra
  • Differential Geometry
  • Research Topics
  • Measure Theory
  • Distributions Theory

Spring 2015/2016:

  • Advanced Numerical Analysis
  • Computational Methods
  • Real Analysis II
  • Measure and Integration
  • Advanced Analysis and Applications
  • Spectral Theory
  • Operation Research

Fall 2016/2017:

  • Mathematical Methods for Physics
  • Mathematical Physics
  • Topology
  • Measure and Integration
  • Finite Element Method
  • Advanced Methods of Applied Math
  • Real Analysis I
  • Linear Algebra

Spring 2016/2017:

  • Differential Calculus (Debbieh + Tripoli)
  • Real Analysis II (Debbieh +Tripoli)
  • Senior Research in Mathematics
  • Senior Project
  • Advanced Analysis &Applications
  • Spectral Theory

Fall 2017/2018:

  • Real Analysis I
  • Linear Algebra
  • Differential Geometry
  • Partial Differential Equations
  • Measure and Integration
  • Advanced Methods of Applied Math

Spring 2017/2018:

  • Biostatistics
  • Real Analysis I(Debbieh + Tripoli)
  • Differential Calculus
  • Senior Project
  • Advanced Analysis &Applications
  • Evolution Seminar

Fall 2018/2019:

  • Real Analysis I
  • Linear Algebra (Debbieh + Beirut)
  • Int. to Calculus & Analytical Geometry II
  • Business Math
  • Measure and Integration
  • Advanced Methods of Applied Math

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.
 
Control theory : Stabilisation of hyperbolic PDEs such as Timoshenko, Bresse, Laminated systems  
 
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 Journal
of Analysis and Applications Vol. 16 (2018), No.1, pp.1-40

14. T. El Arwadi, M. Amine Cherif The Schauder and Krasnoselskii Fixed-Point Theorems on a Frechet Space Mediterranean Journal of Mathematics (2018)15 :121 https ://doi.org/10.1007
 
15. M. Ali Haidar, T. El Arwadi, S. Israwi Existence of a regular solution for 1D Green-Naghdi equations with surface tension Boundary Value Problem
(2018) 2018 : 136. https ://doi.org/10.1186/s13661-018-1055-2
 
16. T. El Arwadi, S. El Kontar, T. Sayyah Improvement of the error estimates for the D-bar method and stability (Submitted)  T. El Arwadi, S. El Kontar, T. Sayah A regularized D-bar method for the Calderon inverse problem with complex conductivity (Submitted)
 
17. T. El Arwadi, T. Sayah A Regularization Scheme for 2D Conductivity Imaging by the D-Bar Method Numerical Functional Analysis and Optimization,
40 :12, 1410-1425, DOI : 10.1080/01630563.2019.1606011
 
18. T. El Arwadi, M.I Copetti, W. Youssef On the theoretical and numerical stability of the thermoviscoelastic Bresse system Z Angew Math Mech. 2019,
99 :e201800207, https ://doi.org/10.1002/zamm.201800207
 
19. T. El Arwadi, W. Youssef On the Stabilization of the Bresse Beam with Kelvin Voigt Damping Appl Math Optim (2019). https ://doi.org/10.1007/s00245-
019-09611-z
 
20. T. El Arwadi, T. Sayah A new regularization of the D-bar method with complex conductivity Complex Variables and Elliptic Equations (2020). https ://doi.org/10.1080/17476933.2020.1747056
 
21.  M.Haidar, T. El Arwadi, S.Israwi Explicit solutions and numerical simulations for an asymptotic water waves model with surface tension J. Appl.
Math. Comput. 63, 655â681 (2020). https ://doi.org/10.1007/s12190-020-01333-8
 
22. M.Bzeih, T. El Arwadi, A. Wehbe, M.Rincon, R.Madureira Numerical analysis and simulation for a wave equation with dynamical boundary control
(Accepted in Journal of Scientific Computing)
 
23. M.Haidar, T. El Arwadi, S.Israwi On the Green Naghdi system with surface tension in the C-H scale (Accepted)
 
24 T. El Arwadi, S. Israwi An explicit solution with correctors for variable depth KdV and Camassa-Holm equations (Accepted)

- 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)